Constraining ultra slow roll inflation using cosmological datasets

CMB temperature fluctuation observations provide a precise measurement of the primordial power spectrum on large scales, corresponding to wavenumbers 10−3 Mpc−1 ≲ k ≲ 0.1 Mpc−1, [1-7, 11]. Luminous red galaxies and galaxy clusters probe the matter power spectrum on overlapping scales (0.02 Mpc−1 ≲ k ≲ 0.7 Mpc−1; [10, 12-20]), while the Lyman-alpha forest reaches slightly smaller scales (0.3 Mpc−1 ≲ k ≲ 3 Mpc−1; [22]). These observations indicate that the primordial power spectrum is nearly scale-invariant with an amplitude close to 2 × 10−9, [5, 23-28]. These observations strongly support Inflation and motivate us to obtain observations and constraints reaching to smaller scales on the primordial curvature power spectrum and by implication on Inflation. We are able to obtain limits to much higher values of k ≲ 105 Mpc−1 and with less sensitivity even higher k ≲ 1019− 1023 Mpc−1 using limits from CMB spectral distortions and other limits on ultracompact minihalo objects (UCMHs) and Primordial Black Holes (PBHs). PBHs are one of the known candidates for the Dark Matter (DM). Due to their very early formation, they could give us valuable information about the primordial curvature perturbations. These are complementary to other cosmological bounds on the amplitude of the primordial fluctuations. In this paper, we revisit and collect all the published constraints on both PBHs and UCMHs. We show that unless one uses the CMB spectral distortion, PBHs give us a very relaxed bounds on the primordial curvature perturbations. UCMHs, on the other hand, are very informative over a reasonable k range (3 ≲ k ≲ 106 Mpc−1) and lead to significant upper-bounds on the curvature spectrum. We review the conditions under which the tighter constraints on the UCMHs could imply extremely strong bounds on the fraction of DM that could be PBHs in reasonable models. Failure to satisfy these conditions would lead to over production of the UCMHs which is inconsistent with the observations. Therefore, we can almost rule out PBH within their overlap scales with the UCMHs. We compare the UCMH bounds coming from those experiments which are sensitive to the nature of the DM, such as γ-rays, Neutrinos and Reionization, with those which are insensitive to the type of the DM, e.g. the pulsar-timing as well as CMB spectral distortion. We explicitly show that they lead to comparable results which are independent of the type of DM. These bounds however do depend on the required initial density perturbation, i.e. δmin. It could be either a constant or a scale-dependent function. As we will show, the constraints differ by three orders of magnitude depend on our choice of required initial perturbations.

We propose a new, likelihood-free approach to inferring the primordial matter power spectrum and cosmological parameters from arbitrarily complex forward models of galaxy surveys where all relevant statistics can be determined from numerical simulations, i.e. black boxes. Our approach, which we call simulator expansion for likelihood-free inference (selfi), builds upon approximate Bayesian computation using a novel effective likelihood, and upon the linearization of black-box models around an expansion point. Consequently, we obtain simple ‘filter equations’ for an effective posterior of the primordial power spectrum, and a straightforward scheme for cosmological parameter inference. We demonstrate that the workload is computationally tractable, fixed a priori, and perfectly parallel. As a proof of concept, we apply our framework to a realistic synthetic galaxy survey, with a data model accounting for physical structure formation and incomplete and noisy galaxy observations. In doing so, we show that the use of non-linear numerical models allows the galaxy power spectrum to be safely fitted up to at least kmax = 0.5 h Mpc−1, outperforming state-of-the-art backward-modelling techniques by a factor of ∼5 in the number of modes used. The result is an unbiased inference of the primordial matter power spectrum across the entire range of scales considered, including a high-fidelity reconstruction of baryon acoustic oscillations. It translates into an unbiased and robust inference of cosmological parameters. Our results pave the path towards easy applications of likelihood-free simulation-based inference in cosmology. We have made our code pyselfi and our data products publicly available at http://pyselfi.florent-leclercq.eu.

Well-known causality arguments show that events occurring during or at the end of inflation, associated with reheating or preheating, could contribute a blue component to the spectrum of primordial curvature perturbations, with the dependence k3. We explore the possibility that they could be observably large in CMB, LSS, and Lyman-α data. We find that a k3 component with a cutoff at some maximum k can modestly improve the fits (Δχ2 = 2.0, 5.4) of the low multipoles (ℓ ~ 10–50) or the second peak (ℓ ~ 540) of the CMB angular spectrum when the three-year WMAP data are used. Moreover, the results from WMAP are consistent with the CBI, ACBAR, 2dFGRS, and SDSS data when they are included in the analysis. Including the SDSS galaxy clustering power spectrum, we find weak positive evidence for the k3 component at the level of Δχ2′ = 2.4, with the caveat that the nonlinear evolution of the power spectrum may not be properly treated in the presence of the k3 distortion. To investigate the high-k regime, we use the Lyman-α forest data (LUQAS, Croft et al., and SDSS Lyman-α); here we find evidence at the level Δχ2′ = 3.8. Considering that there are two additional free parameters in the model, the above results do not give a strong evidence for features; however, they show that surprisingly large bumps are not ruled out. We give constraints on the ratio between the k3 component and the nearly scale-invariant component, r3 < 1.5, over the range of wave numbers 2.3 × 10-3 Mpc -1 < k < 8.2 Mpc -1. We also discuss theoretical models which could lead to the k3 effect, including ordinary hybrid inflation and double D-term inflation models. We show that the well-motivated k3 component is also a good representative of the generic spikelike feature in the primordial perturbation power spectrum.

In light of the latest Planck and Atacama Cosmology Telescope (P-ACT) joint results on the primordial scalar power spectrum, we show that the R 2 inflation model extended with a non-minimally coupled scalar field χ — namely the χ-extended R 2 inflation model — can naturally accommodate a larger spectral index ns and a small positive running αs at cosmic microwave background (CMB) scales, both of which are consistent with the latest P-ACT constraints. This is because the χ field contributes a blue-tilted component to the primordial power spectrum, which both modifies the large-scale power and, as a result, significantly enhances power on small scales. The deviation of the ns and αs from the single field R 2 inflation is related to the non-minimal coupling constant ξ. The consequent enhancement in the primordial power spectrum can be large enough to lead to the formation of primordial black holes (PBHs) of mass ≲1020 g as dark matter candidates. Furthermore, future observations of the small-scale power spectrum, CMB spectral distortions, and stochastic gravitational waves will provide decisive tests of this model and its predictions for PBHs. We stress its strong connection to the seesaw mechanism for the generation of the observed small masses.

Observational constraints on the abundance of primordial black holes (PBHs) constrain the allowed amplitude of the primordial power spectrum on both the smallest and the largest ranges of scales, covering over 20 decades from 1−1020/ Mpc. Despite tight constraints on the allowed fraction of PBHs at their time of formation near horizon entry in the early Universe, the corresponding constraints on the primordial power spectrum are quite weak, typically \U0001d4abR≲ 10−2 assuming Gaussian perturbations. Motivated by recent claims that the evaporation of just one PBH would destabilise the Higgs vacuum and collapse the Universe, we calculate the constraints which follow from assuming there are zero PBHs within the observable Universe. Even if evaporating PBHs do not collapse the Universe, this scenario represents the ultimate limit of observational constraints. Constraints can be extended on to smaller scales right down to the horizon scale at the end of inflation, but where power spectrum constraints already exist they do not tighten significantly, even though the constraint on PBH abundance can decrease by up to 46 orders of magnitude. This shows that no future improvement in observational constraints can ever lead to a significant tightening in constraints on inflation (via the power spectrum amplitude). The power spectrum constraints are weak because an order unity perturbation is required in order to overcome pressure forces. We therefore consider an early matter dominated era, during which exponentially more PBHs form for the same initial conditions. We show this leads to far tighter constraints, which approach \U0001d4abR≲10−9, albeit over a smaller range of scales and are very sensitive to when the early matter dominated era ends. Finally, we show that an extended early matter era is incompatible with the argument that an evaporating PBH would destroy the Universe, unless the power spectrum amplitude decreases by up to ten orders of magnitude.

High-$z$ galaxy redshift surveys open up exciting possibilities for precision determinations of neutrino masses and inflationary models. The high-$z$ surveys are more useful for cosmology than low-$z$ ones owing to much weaker nonlinearities in matter clustering, redshift-space distortion, and galaxy bias, which allows us to use the galaxy power spectrum down to the smaller spatial scales that are inaccessible by low-$z$ surveys. We can then utilize the two-dimensional information of the linear power spectrum in angular and redshift space to measure the scale-dependent suppression of matter clustering due to neutrino free-streaming as well as the shape of the primordial power spectrum. To illustrate capabilities of high-$z$ surveys for constraining neutrino masses and the primordial power spectrum, we compare three future redshift surveys covering 300 square degrees at $0.5lzl2$, $2lzl4$, and $3.5lzl6.5$. We find that, combined with the cosmic microwave background data expected from the Planck satellite, these surveys allow precision determination of the total neutrino mass with the projected errors of $\ensuremath{\sigma}({m}_{\ensuremath{\nu},\mathrm{tot}})=0.059$, 0.043, and 0.025 eV, respectively, thus yielding a positive detection of the neutrino mass rather than an upper limit, as $\ensuremath{\sigma}({m}_{\ensuremath{\nu},\mathrm{tot}})$ is smaller than the lower limits to the neutrino masses implied from the neutrino oscillation experiments, by up to a factor of 4 for the highest redshift survey. The accuracies of constraining the tilt and running index of the primordial power spectrum, $\ensuremath{\sigma}({n}_{s})=(3.8,3.7,3.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $\ensuremath{\sigma}({\ensuremath{\alpha}}_{s})=(5.9,5.7,2.4)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at ${k}_{0}=0.05\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$, respectively, are smaller than the current uncertainties by more than an order of magnitude, which will allow us to discriminate between candidate inflationary models. In particular, the error on ${\ensuremath{\alpha}}_{s}$ from the future highest redshift survey is not very far away from the prediction of a class of simple inflationary models driven by a massive scalar field with self-coupling, ${\ensuremath{\alpha}}_{s}=\ensuremath{-}(0.8\char21{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

Although the standard $\mathrm{\ensuremath{\Lambda}}+\mathrm{cold}$ dark matter ($\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$) model is well tested on large scales, the primordial power spectrum may deviate from the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ spectrum on small scales due to specific dark matter properties or alternative inflationary models. These deviations affect the formation of dark matter structure, which subsequently leads to different observable properties of galaxies. In this work, we study the impact of a blue and red tilted power spectrum on the central density of dwarf galaxies. To do this, we model densities of dwarf galaxies using a combination of high-resolution numerical simulations and galaxy formation model. The model galaxies in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ are consistent with observations of 41 faint dwarf satellite galaxies of the Milky Way. The deviations from the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ power spectrum are constrained by the central matter densities of dwarf galaxies, which set stringent constraints on the possible small-scale tilt of the primordial power spectrum, improving on the current limits. Moreover, similar analysis can be applied to test any feature in the power spectrum at small scales between $k\ensuremath{\sim}10--100\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$.

The ultra-slow-roll (USR) inflationary models predict large-amplitude scalar perturbations at small scales which can lead to the primordial black hole production and scalar-induced gravitational waves. In general scalar perturbations in the USR models can only be obtained using numerical method because the usual slow-roll approximation breaks. In this work, we propose an analytical approach to estimate the scalar spectrum which is consistent with the numerical result. We find that the USR inflationary models predict a peak with power-law slopes in the scalar spectrum and energy spectrum of gravitational waves, and we derive the expression of the spectral indexes in terms of the inflationary potential. In turn, the inflationary potential near the USR regime can be reconstructed from the negative spectral index of the gravitational wave energy spectrum.

We calculate the mean power spectrum of all galaxies using published power spectra of galaxies and clusters of galaxies. On small scales we use the power spectrum derived from the two-dimensional distribution of Automatic Plate Measuring Facility (APM) galaxies, since this sample is not influenced by redshift distortions and is the largest and deepest sample of galaxies available. On large scales we use power spectra derived from three-dimensional data for various galaxy and cluster samples which are reduced to real space and in amplitude to the power spectrum of APM galaxies. We find that available data indicate the presence of two different populations in the nearby universe. Clusters of galaxies sample a relatively large region in the universe where rich, medium, and poor superclusters are well represented. Their mean power spectrum has a spike at wavenumber k = 0.05 ± 0.01 h Mpc-1, followed by an approximate power-law spectrum of index n ≈ -1.9 toward small scales. Some galaxy surveys (APM three-dimensional, IRAS QDOT, and SSRS+CfA2 130 Mpc) have similar spectra. The power spectrum found from the Las Campanas Redshift Survey and IRAS 1.2 Jy surveys is flatter around the maximum, which may represent regions of the universe with medium-rich and poor superclusters. Differences in power spectra for these populations may partly be due to the survey geometries of the data sets in question and/or to features of the original data analysis.

We revisit the one-loop correction in curvature perturbation power spectrum in models of single field inflation which undergo a phase of ultra slow-roll (USR) inflation. We include the contributions from both the cubic and quartic interaction Hamiltonians and calculate the one-loop corrections on the spectrum of the CMB scale modes from the small scale modes which leave the horizon during the USR phase. It is shown that the amplitude of one-loop corrections depends on the sharpness of the transition from the USR phase to the final slow-roll phase. For an arbitrarily sharp transition, the one-loop correction becomes arbitrarily large, invalidating the perturbative treatment of the analysis. We speculate that for a mild transition, the large one-loop corrections are washed out during the subsequent evolution after the USR phase. The implications for primordial black holes formation are briefly reviewed.

A class of inflationary models that involve rapid bursts of particle productions predict observational signatures, such as bump-like features in the primordial scalar power spectrum. In this work, we analyze such models by comparing their predictions with the latest CMB data from Planck 2018. We consider two scenarios of particle production. The first one is a simple scenario consisting of a single burst of particle production during observable inflation. The second one consists of multiple bursts of particle production that lead to a series of bump-like features in the primordial power spectrum. We find that the second scenario of the multi-bump model gives better fit to the CMB data compared to the concordance ΛCDM model. We carried out model comparisons using Bayesian evidences. From the observational constraints on the amplitude of primordial features of the multi-bump model, we find that the dimensionless coupling parameter g responsible for particle production is bound to be g < 0.05.

We investigate the ability of current cosmic microwave background data to reliablyconstrain the form of the primordial power spectrum generated during inflation. Weattempt to identify more exotic power spectra that yield equally good fits to the data assimple power-law spectra. In order to test a wide variety of spectral shapes, we combine theflow formalism, which is a method of stochastic model generation, with a numericalintegration of the mode equations of quantum fluctuations. This allows us to handleinflation models that yield spectra that are not well described by the standard spectralparameterization. Using the latest WMAP data set, we find a high degree of variation inpossible spectral shapes. In particular, we find strongly running spectra arising fromfast-rolling inflaton fields providing equally good fits to the data as power-law spectraarising from slowly rolling fields. Current data poorly constrains the spectrum on scalesk<0.01h Mpc−1, where the error due to cosmic variance is large. Among the statistically degeneratemodels, we identify spectra with strong running on these larger scales, but with reducedrunning at smaller scales. These models predict values for the tensor-to-scalar ratio,r, that lieoutside the 2-σ confidence interval obtained from SDSS + WMAP (Sloan Digital Sky Survey plusWilkinson Microwave Anisotropy Probe) data for spectra that are parameterized as powerlaws or spectra with constant running. By considering more generalized powerspectra, we therefore open up regions of parameter space excluded for simplermodels.

Here, we explore the formation of primordial black holes (PBHs) within a scalar field inflationary model coupled to the Gauss-Bonnet (GB) term, incorporating the low-scale spontaneously broken supersymmetric (SB SUSY) potential.The coupling function amplifies the curvature perturbations, consequently leading to the formation of PBHs and detectable secondary gravitational waves (GWs).Through the adjustment of the model parameters, the inflaton can be decelerated during an ultra-slow-roll (USR) phase, thereby augmenting curvature perturbations. Beside the observational constraints, the swampland criteria are investigated.Our computations forecast the formation of PBHs with masses around 𝒪(10)M ⊙, aligning with the observational data of LIGO-Virgo, and PBHs with masses 𝒪(10-6)M ⊙ as potential explanation for the ultrashort-timescale microlensing events recorded in the OGLE data.Additionally, our proposed mechanism can generate PBHs with masses around 𝒪(10-13)M ⊙, constituting roughly 99% of the dark matter.The density parameters of the produced GWs (ΩGW 0) intersect with the sensitivity curves of GW detectors. Two cases of our model fall within the nano-Hz frequency regime. One of them satisfies the power-law scaling as ΩGW(f) ∼ f 5-γ, with the γ = 3.51, which is consistent with the data of NANOGrav 15-year.

The highly redshifted 21 cm line of neutral hydrogen has become recognized as\na unique probe of cosmology from relatively low redshifts (z ~ 1) up through\nthe Epoch of Reionization (z ~ 8) and even beyond. To date, most work has\nfocused on recovering the spherically averaged power spectrum of the 21 cm\nsignal, since this approach maximizes the signal-to-noise in the initial\nmeasurement. However, like galaxy surveys, the 21 cm signal is affected by\nredshift space distortions, and is inherently anisotropic between the\nline-of-sight and transverse directions. A measurement of this anisotropy can\nyield unique cosmological information, potentially even isolating the matter\npower spectrum from astrophysical effects. However, in interferometric\nmeasurements, foregrounds also have an anisotropic footprint between the\nline-of-sight and transverse directions: the so-called foreground "wedge".\nAlthough foreground subtraction techniques are actively being developed, a\n"foreground avoidance" approach of simply ignoring contaminated modes has\narguably proven most successful to date. In this work, we analyze the effect of\nthis foreground anisotropy in recovering the redshift space distortion\nsignature in 21 cm measurements at both high and intermediate redshifts. We\nfind the foreground wedge corrupts nearly all of the redshift space signal for\neven the largest proposed EoR experiments (HERA and the SKA), making\ncosmological information unrecoverable without foreground subtraction. The\nsituation is somewhat improved at lower redshifts, where the redshift-dependent\nmapping from observed coordinates to cosmological coordinates significantly\nreduces the size of the wedge. Using only foreground avoidance, we find that a\nlarge experiment like CHIME can place non-trivial constraints on cosmological\nparameters.\n

We develop a phase space distribution function approach to redshift space distortions (RSD), in which the redshift space density can be written as a sum over velocity moments of the distribution function. These moments are density weighted and have well defined physical interpretation: their lowest orders are density, momentum density, and stress energy density. The series expansion is convergent if kμu/aH < 1, where k is the wavevector, H the Hubble parameter, u the typical gravitational velocity and μ = cos θ, with θ being the angle between the Fourier mode and the line of sight. We perform an expansion of these velocity moments into helicity modes, which are eigenmodes under rotation around the axis of Fourier mode direction, generalizing the scalar, vector, tensor decomposition of perturbations to an arbitrary order. We show that only equal helicity moments correlate and derive the angular dependence of the individual contributions to the redshift space power spectrum. We show that the dominant term of μ2 dependence on large scales is the cross-correlation between the density and scalar part of momentum density, which can be related to the time derivative of the matter power spectrum. Additional terms contributing to μ2 and dominating on small scales are the vector part of momentum density-momentum density correlations, the energy density-density correlations, and the scalar part of anisotropic stress density-density correlations. The second term is what is usually associated with the small scale Fingers-of-God damping and always suppresses power, but the first term comes with the opposite sign and always adds power. Similarly, we identify 7 terms contributing to μ4 dependence. Some of the advantages of the distribution function approach are that the series expansion converges on large scales and remains valid in multi-stream situations. We finish with a brief discussion of implications for RSD in galaxies relative to dark matter, highlighting the issue of scale dependent bias of velocity moments correlators.