TESTING FOR FEATURES IN THE PRIMORDIAL POWER SPECTRUM

We analytically compute the power spectrum of primordial curvature perturbations in Type III hilltop inflation models under the slow-roll approximation. The model parameters are constrained using current Cosmic Microwave Background (CMB) data. The curvature perturbations that exit the horizon at small scales show sufficiently large amplitudes to produce primordial black holes (PBHs). We then consider the quantum one-loop corrections in these models from both the self-interaction of the inflaton and its interaction with the waterfall field. We show the loop corrections in both cases for 60 e-folds of inflation are negligible, ensuring the tree-level results are reliable within the chosen parameter regime.

Constraints on inflation from cosmic microwave background and Lyman-α forest

The primordial black hole (PBH) is an effective candidate for dark matter. In this work, the PBH abundance $f$ is calculated in peak theory, with one or two perturbations in the inflaton potential. We construct an antisymmetric perturbation that can create a perfect plateau in the inflaton potential, leading inflation to the ultraslow-roll stage. During this stage, the power spectrum of primordial curvature perturbation is remarkably enhanced on small scales, generating abundant PBHs. The PBH abundance $f\ensuremath{\sim}0.1$ can be achieved in one or two typical mass windows at ${10}^{\ensuremath{-}17}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, ${10}^{\ensuremath{-}13}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, and $30\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, without spoiling the nearly scale-invariant power spectrum on large scales. For comparison, $f$ is calculated in two approximate methods of peak theory (with different spectral moments) and also in the Press-Schechter theory. It is found that the Press-Schechter theory systematically underestimates $f$ by 2 or 3 orders of magnitude compared with peak theory.

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.

Primordial black holes (PBHs) are mainly characterized by their mass function, in which there may be some huge suppression for certain mass spans. If this is the case, the absence of these PBHs will form mass gaps. In this paper, we investigate the PBH mass function with the mass gap. First, to obtain a data-supported PBH mass function with the mass gap for subsolar masses PBHs, we fine-tune the coefficients of a model-independent power spectrum of primordial curvature perturbations. Then we take this unique PBH mass function into consideration and calculate the energy-density spectrum of the stochastic gravitational-wave background from PBH mergers. We find the location of its first peak almost has no relationship with the mass gap and is only determined by the probability distribution of frequencies at which PBH binaries merge. Apart from the first peak, there must be an accompanying smaller trough at a higher frequency resulting from the mass gap. Therefore, the detection of this smaller trough will provide more information about inflation and PBH formation.

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.

Effects of features in the inflaton potential on the spectrum and bispectrum of primordial curvature perturbations

Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum is preferred by current observations, and hence non-power-law models ought to be considered. For instance, for a power-law parameterisation with both a tensor component and running parameter, current data show a preference for a negative running at more than 2.5σ C.L. As a consequence of this deviation from a power-law, constraints on the tensor-to-scalar ratio r are slightly broader. We also present constraints on the inflationary parameters for a model-independent reconstruction and the Lasenby & Doran (LD) model. In particular, the constraints on the tensor-to-scalar ratio from the LD model are: rLD = 0.11±0.024. In addition to current data, we show expected constraints from Planck-like and CMB-Pol sensitivity experiments by using Markov-Chain-Monte-Carlo sampling chains. For all the models, we have included the Bayesian Evidence to perform a model selection analysis. The Bayes factor, using current observations, shows a strong preference for the LD model over the standard power-law parameterisation, and provides an insight into the accuracy of differentiating models through future surveys.

The properties of the recently discovered Higgs boson together with the absence of new physics at collider experiments allows us to speculate about consistently extending the Standard Model of particle physics all the way up to the Planck scale. In this context, the Standard Model Higgs non-minimally coupled to gravity could be responsible for the symmetry properties of the Universe at large scales and for the generation of the primordial spectrum of curvature perturbations seeding structure formation. We overview the minimalistic Higgs inflation scenario, its predictions, open issues and extensions and discuss its interplay with the possible metastability of the Standard Model vacuum.

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.

We study the background dynamics and primordial perturbation in $\alpha$-attractor-type double inflation. The model is composed of two minimally coupled scalar fields, where each of the fields has a potential of the $\alpha$-attractor type. We find that the background trajectory in this double inflation model is given by two almost straight lines connected with a turn in the field space. With this simple background, we can classify the property of the perturbations generated in this double inflation model just depending on whether the turn occurs before the horizon exit for the mode corresponding to the scale of interest or not. In the former case, the resultant primordial curvature perturbation coincides with the one obtained by the single-field $\alpha$-attractor. On the other hand, in the latter case, it is affected by the multifield effects, like the mixing with the isocurvature perturbation and the change of the Hubble expansion rate at the horizon exit. We obtain the approximated analytic solutions for the background, with which we can calculate the primordial curvature perturbation by the $\delta N$ formalism analytically, even when the multifield effects are significant. We also impose observational constraints on the model parameters and initial values of the fields in this double inflation model based on the Planck result.

We study the generation of the primordial curvature perturbation in multi-field inflation. Considering both the evolution of the perturbation during inflation and the effects generated at the end of inflation, we present a general formula for the curvature perturbation. We provide the analytic expressions of the power spectrum, spectral tilt and non-Gaussianity for the separable potentials of two inflaton scalars, and apply them to some specific models.

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.

Current cosmological observations are remarkably consistent with a concordance cosmology including an epoch of inflation in the very early universe. There is a tantalizing possibility that the ultra-high energy physics of the very early universe could be deduced from cosmological observations. In particular, the observed angular power spectrum of the CMB anisotropy is a convolution of the cosmological radiative transport kernel with the power spectrum of primordial perturbations. Exquisite measurements of the angular power spectrum over a wide range of multipoles from WMAP have opened up the possibility to deconvolve the primordial power spectrum for a given set of cosmological parameters. We present an update on our ongoing research program to recover the primordial power spectrum from CMB anisotropy. The robust features in the recovered primordial spectrum could be signatures of the physics behind inflation. Initial work towards mapping out the likelihood, ‘optimized’ over the unknown primordial spectrum, in the space the cosmological parameters reveal interesting results.

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.