Limits on primordial power spectrum resolution: an inflationary flow analysis

The new 3 year WMAP data seem to confirm the presence of nonstandard large scale features in the cosmic microwave anisotropy power spectrum. While these features may hint at uncorrected experimental systematics, it is also possible to generate, in a cosmological way, oscillations on large angular scales by introducing a sharp step in the inflaton potential. Using current cosmological data, we derive constraints on the position, magnitude and gradient of a possible step. We show that a step in the inflaton potential, while strongly constrained by current data, is still allowed and may provide an interesting explanation to the currently measured deviations from the standard featureless spectrum. Moreover, we show that inflationary oscillations in the primordial power spectrum can significantly bias parameter estimates from standard ruler methods involving measurements of baryon oscillations.

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.

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.

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.

Features in the primordial power spectrum have been suggested as an explanation for glitches in the angular power spectrum of temperature anisotropies measured by the WMAP satellite. However, these glitches might just as well be artifacts of noise or cosmic variance. Using the effective Δχ2 between the best-fit power-law spectrum and a deconvolved primordial spectrum as a measure of ``featureness'' of the data, we perform a full Monte-Carlo analysis to address the question of how significant the recovered features are. We find that in 26% of the simulated data sets the reconstructed spectrum yields a greater improvement in the likelihood than for the actually observed data. While features cannot be categorically ruled out by this analysis, and the possibility remains that simple theoretical models which predict some of the observed features might stand up to rigorous statistical testing, our results suggest that WMAP data are consistent with the assumption of a featureless power-law primordial spectrum.

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 $k\ensuremath{\sim}10--100\text{ }\text{ }{\mathrm{Mpc}}^{\ensuremath{-}1}$.

We analyse the abundance of right-handed sneutrinos in the supersymmetric FD-term model of hybrid inflation. As well as providing a natural solution to the μ- and gravitino overabundance problems, the model offers the lightest right-handed sneutrino as a candidate for thermal dark matter. The FD-term model predicts a new quartic coupling of purely right-handed sneutrinos to the Higgs doublets that thermalises the sneutrinos and makes them annihilate sufficiently fast to a level compatible with the current cosmic microwave background data. We discuss this scenario and identify favourable regions of the parameter space within mSUGRA.

In recent years, the detection of gravitational waves by LIGO and PTA collaborationshave raised the intriguing possibility of excess matter power at small scales. Such anincrease can be achieved by ultra slow roll (USR) phase during inflationary epoch.We constrain excess power over small scales within the framework of such models usingcosmological datasets, particularly of CMB anisotropies and Lyman-α.We parameterize the USR phase in terms of thee-fold at the onset of USR (counted from the end of inflation) N̅1 andthe duration of USR phase Δ N.The former dictates the scale of enhancement in the primordial power spectrum, while the latter determines the amplitude of such anenhancement.From a joint dataset of CMB and galaxy surveys, we obtainN̅1 ≲ 45 with no bound on Δ N. This in turn implies thatthe scales over which the power spectrum can deviate significantly from thenearly scale invariant behavior of a typical slow-roll model isk ≳1 Mpc-1.On the other hand, the Lyman-α data is sensitive to baryonic powerspectrum along the line of sight. We consider a semi-analytic theoretical methodand high spectral-resolution Lyman-α data to constrain the model.The Lyman-α data limits both the USR parameters:N̅1 ≲ 41 and Δ N ≲ 0.4.This constrains the amplitude of the power spectrum enhancement to be less thana factor of hundred over scales 1 ≲ k/ Mpc-1≲ 100,thereby considerably improving the constraint on power over these scales ascompared to the bounds arrived at from CMB spectral distortion.

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 consider two stable Interacting Dark Matter-Dark Energy models and confront them against current Cosmic Microwave Background data from the Planck satellite. We then generate luminosity distance measurements from \U0001d4aa(103) mock Gravitational Wave events matching the expected sensitivity of the proposed Einstein Telescope. We use these to forecast how the addition of Gravitational Wave standard sirens data can improve current limits on the Dark Matter-Dark Energy coupling strength (ξ). We find that the addition of Gravitational Waves data can reduce the current uncertainty by a factor of 5. Moreover, if the underlying cosmological model truly features Dark Matter-Dark Energy interactions with a value of ξ within the currently allowed 1σ upper limit, the addition of Gravitational Wave data would help disentangle such an interaction from the standard case of no interaction at a significance of more than 3σ.

Spectroscopic studies of high-redshift objects and increasingly precise data on the cosmic microwave background (CMB) are beginning to independently place strong complementary bounds on the epoch of hydrogen reionization. Parameter estimation from current CMB data continues, however, to be subject to several degeneracies. Here, we focus on those degeneracies in CMB parameter forecasts related to the optical depth to reionization. We extend earlier work on the mutual constraints that such analyses of CMB data and a reionization model may place on each other to a more general parameter set, and to the case of data anticipated from the $MAP$ satellite. We focus in particular on a semi-analytic model of reionization by the first stars, although the methods here are easily extended to other reionization scenarios. A reionization model can provide useful complementary information for cosmological parameter (CP) extraction from the CMB, particularly for the degeneracies between the optical depth and either of the amplitude and index of the primordial scalar power spectrum, which are still present in the most recent data. Alternatively, by using a reionization model, known limits on astrophysical quantities can reduce the forecasted errors on CPs. Forthcoming CMB data also have the potential to constrain the sites of early star formation, as well as the fraction of baryons that participate in it. Finally, we examine the implications of an independent, e.g., spectroscopic, determination of the epoch of reionization for the determination of CPs from the CMB. This has the potential to significantly strengthen limits from the CMB on parameters such as the index of the power spectrum, while having the considerable advantage of being free of the choice of the reionization model (abridged).

We present a simple inflationary scenario that can produce arbitrarily large spherical underdense or overdense regions embedded in a standard Λ cold dark matter paradigm, which we refer to as bubbles. We analyze the effect such bubbles would have on the Cosmic Microwave Background (CMB). For super-horizon sized bubble in the vicinity of the last scattering surface, a signal is imprinted onto CMB via a combination of Sach-Wolfe and an early integrated Sach-Wolfe (ISW) effects. Smaller, sub-horizon sized bubbles at lower redshifts (during matter domination and later) can imprint secondary anisotropies on the CMB via Rees-Sciama, late-time ISW and Ostriker-Vishniac effects. Our scenario, and arguably most similar inflationary models, produce bubbles which are over/underdense in potential: in density such bubbles are characterized by having a distinct wall with the interior staying at the cosmic mean density. We show that such models can potentially, with only moderate fine tuning, explain the cold spot, a non-Gaussian feature identified in the Wilkinson Microwave Anisotropy Probe (WMAP) data by several authors. However, more detailed comparisons with current and future CMB data are necessary to confirm (or rule out) this scenario.

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, ${\ensuremath{\alpha}}_{s}=\ensuremath{-}(0.8\char21{}1.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

We continue the study of mild transient reductions in the speed of sound of the adiabatic mode during inflation, of their effect on the primordial power spectrum and bispectrum, and of their detectability in the cosmic microwave background (CMB). We focus on the regime of moderately sharp mild reductions in the speed of sound during uninterrupted slow-roll inflation, a theoretically well motivated and self-consistent regime that admits an effective single-field description. The signatures on the power spectrum and bispectrum were previously computed using a slow-roll Fourier transform (SRFT) approximation, and here we compare it with generalized slow roll and in-in methods, for which we derive new formulas that account for moderately sharp features. The agreement between them is excellent, and also with the power spectrum obtained from the numerical solution to the equation of motion. We show that, in this regime, the SRFT approximation correctly captures with simplicity the effect of higher derivatives of the speed of sound in the mode equation, and makes manifest the correlations between power spectrum and bispectrum features. In a previous paper we reported hints of these correlations in the Planck data and here we perform several consistency checks and further analyses of the best fits, such as polarization and local significance at different angular scales. For the data analysis, we show the excellent agreement between the CLASS and CAMB Boltzmann codes. Our results confirm that the theoretical framework is consistent, and they suggest that the predicted correlations are robust enough to be searched for in CMB and large scale structure surveys.

We present a new approach to computing the matter density power spectrum,\nfrom large linear scales to small highly nonlinear scales. Instead of\nexplicitly computing a partial series of high-order diagrams, as in\nperturbative resummation schemes, we embed the standard perturbation theory\nwithin a realistic nonlinear Lagrangian-space ansatz. We also point out that an\n"adhesion-like" regularization of the shell-crossing regime is more realistic\nthan a "Zel'dovich-like" behavior, where particles freely escape to infinity.\nThis provides a "cosmic web" power spectrum with good small-scale properties\nthat provide a good matching with a halo model on mildly nonlinear scales. We\nobtain a good agreement with numerical simulations on large scales, better than\n3% for $k\\leq 1 h$Mpc$^{-1}$, and on small scales, better than 10% for $k \\leq\n10 h$Mpc$^{-1}$, at $z \\geq 0.35$, which improves over previous methods.\n