Primordial Power Spectrum Research Articles

Constraints on dark matter from dynamical heating of stars in ultrafaint dwarfs. II. Substructure and the primordial power spectrum

There is a large and growing interest in observations of small-scale structure in dark matter. We propose a new way to probe dark matter structures in the ∼10–108M⊙ range. This allows us to constrain the primordial power spectrum over shorter distances scales than possible with direct observations from the CMB. For k in the range ∼10–1000 Mpc−1 our constraints on the power spectrum are orders of magnitude stronger than previous bounds. We also set some of the strongest constraints on dark matter isocurvature perturbations. Our method relies on the heating effect such dark matter substructures would have on the distribution of stars in an ultrafaint dwarf galaxy. Many models of inflation produce enhanced power at these short distance scales and can thus be constrained by our observation. Further, many dark matter models such as axion dark matter, self-interacting dark matter and dissipative dark matter, produce dense structures which could be constrained this way. Published by the American Physical Society 2024

A natural model for curved inflation

Abstract Inflationary models with a non-zero background curvature require additional hy- pothesis or parameters compared to flat inflation and the procedure to construct them cannot be as simple as in the flat case. For this reason, there is no consen- sus on the primordial power spectrum that should be considered at large scales in a curved Universe. In this letter, we propose a model of curved inflation in which the usual canonical quantization and Bunch–Davies vacuum choice of the flat case can be considered. The framework is a recently proposed modification of general relativity in which a non-dynamical topological term is added to the Einstein equation. The model is universal as it is the same for any background curvature, and no additional parameters or hypothesis on the initial spatial curvature are introduced. This gives a natural and simple solution to the problem of constructing curved inflation, and at the same time provides an additional argument for this topological modification of general relativity.

Analytic Primordial Power Spectrum in the Dressed Metric Approach to Loop Quantum Cosmology and Thermodynamics of Spacetime

Analytic Primordial Power Spectrum in the Dressed Metric Approach to Loop Quantum Cosmology and Thermodynamics of Spacetime

Induced gravitational waves: the effect of first order tensor perturbations

Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to constrain models of inflation. These waves are sourced by terms quadratic in perturbations and hence appear at second order in cosmological perturbation theory. While the focus of research so far was on purely scalar source terms we also study the effect of including first order tensor perturbations as an additional source. This gives rise to two additional source terms: a term quadratic in the tensor perturbations and a cross term involving mixed scalar and tensor perturbations. We present full analytical expressions for the spectral density of these new source terms and discuss their general behaviour. To illustrate the generation mechanism we study two toy models containing a peak on small scales. For these models we show that the scalar-tensor contribution becomes non-negligible compared to the scalar-scalar contribution on smaller scales. We also consider implications for future gravitational wave surveys.

Climbing over the potential barrier during inflation via null energy condition violation

The violation of the null energy condition (NEC) may play a crucial role in enabling a scalar field to climb over high potential barriers, potentially significant in the very early universe. We propose a single-field model where the universe sequentially undergoes a first stage of slow-roll inflation, NEC violation, and a second stage of slow-roll inflation. Through the NEC violation, the scalar field climbs over high potential barriers, leaving unique characteristics on the primordial gravitational wave power spectrum, including a blue-tilted nature in the middle-frequency range and diminishing oscillation amplitudes at higher frequencies. Additionally, the power spectrum exhibits nearly scale-invariant behavior on both large and small scales.

New probe of non-Gaussianities with primordial black hole induced gravitational waves

We propose a new probe of primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light (MPBH<109g) primordial black holes (PBHs). Interestingly enough, the existence of primordial NG can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. Focusing on a scale-dependent local-type NG, we identify a distinct double-peaked GW energy spectrum that, contingent upon MPBH and the abundance of PBHs at the time of formation, denoted as ΩPBH,f, may fall into the frequency bands of upcoming GW observatories, including LISA, ET, SKA, and BBO. Thus, such a signal can serve as a novel portal for probing primordial NGs. Intriguingly, combining BBN bounds on the GW amplitude, we find for the first time the joint limit on the product of the effective non-linearity parameter for the primordial tri-spectrum, denoted by τ¯NL, and the primordial curvature perturbation power spectrum PR(k), which reads as τ¯NLPR(k)<4×10−20ΩPBH,f−17/9(MPBH104g)−17/9.

Primordial black hole interpretation in subsolar mass gravitational wave candidate SSM200308

In the recent second part of the third observation run by the LIGO-Virgo-KAGRA collaboration, a candidate with sub-solar mass components was reported, which we labelled as SSM200308. This study investigates the premise that primordial black holes (PBHs), arising from Gaussian perturbation collapses, could explain SSM200308. Through Bayesian analysis, we obtain the primordial curvature power spectrum that leads to the merger rate of PBHs aligning with observational data as long as they constitute f PBH = 5.66+58.68 -5.44 × 10-2 of the dark matter. However, while the gravitational wave (GW) background from binary PBH mergers is within current observational limits, the scalar-induced GWs associated with PBH formation exceed the constraints imposed by pulsar timing arrays, challenging the Gaussian perturbation collapse PBH model as the source of SSM200308.

Fingerprints of a non-inflationary universe from massive fields

We construct explicit models of classical primordial standard clocks in an alternative to inflation, namely the slowly contracting ekpyrotic scenario. We study the phenomenology of massive spectator fields added to a state-of-the-art ekpyrotic model, with coupling functions that allow for these heavy fields to be classically excited while the background is slowly contracting. We perform numerical computations of the corrections to the scalar primordial power spectrum and compare with analytical estimates. Our full numerical results reveal so-called clock signals, sharp feature signals, as well as signals that link the two together. The models are found to predict oscillatory features that are resolutely different from what is calculated in inflation, and thus, such features represent unique fingerprints of a slowly contracting universe. This confirms the capability of primordial standard clocks to model-independently discriminate among very early universe scenarios.

Renormalization of the primordial inflationary power spectra

It has been suggested that the effects of renormalization significantly reduce the amplitude of the inflationary spectra at scales measurable in the cosmic microwave background. Via a gauge-invariant analysis, we compute the renormalized scalar and tensor power spectra and follow their evolution in an inflating universe that undergoes a transition to an FRW phase with a growing horizon. For perturbations originating from Minkowski vacuum fluctuations, we show that the standard prediction for the spectra on superhorizon scales is a late-time attractor, while they are UV finite at all times. Our result is independent of the equation of state after inflation, showing that the standard prediction is fully robust.

Non-Gaussianity consistency relations and their consequences for the peaks

Strong deviations from scale invariance and the appearance of high peaks in the primordial power spectrum have been extensively studied for generating primordial black holes (PBHs) or gravitational waves (GWs). It is also well-known that the effect of non-linearities can be significant in both phenomena. In this paper, we advocate the existence of a general single-field consistency relation that relates the amplitude of non-Gaussianity in the squeezed limit f NL to the power spectrum and remains valid when almost all other consistency relations are violated. In particular, it is suitable for studying scenarios where scale invariance is strongly violated.We discuss the general and model-independent consequences of the consistency relation on the behavior of f NL at different scales.Specifically, we study the size, sign and slope of f NL at the scales where the power spectrum peaks and argue that generally the peaks of f NL and the power spectrum occur at different scales.As an implication of our results, we argue that non-linearities can shift or extend the range of scales responsible for the production of PBHs or GWs, relative to the window as determined by the largest peak of the power spectrum, and may also open up new windows for both phenomena.

Primordial Black Holes from Null Energy Condition Violation during Inflation.

Primordial black holes (PBHs) and the violation of the null energy condition (NEC) have significant implications for our understanding of the very early Universe. We present a novel approach to generate PBHs via the NEC violation in a single-field inflationary scenario. In our scenario, the Universe transitions from a first slow-roll inflation stage with a Hubble parameter H=H_{inf1} to a second slow-roll inflation stage with H=H_{inf2}≫H_{inf1}, passing through an intermediate stage of NEC violation. The NEC violation naturally enhances the primordial scalar power spectrum at a certain wavelength, leading to the production of PBHs with masses and abundances of observational interest. We also investigate the phenomenological signatures of scalar-induced gravitational waves resulting from the enhanced density perturbations. Our work highlights the potential of utilizing a combination of PBHs, scalar-induced gravitational waves, and primordial gravitational waves as a valuable probe for studying NEC violation during inflation, opening up new avenues for exploring the early Universe.

Constraining ultra slow roll inflation using cosmological datasets

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.

Cosmic Inflation at the crossroads

The capability of Cosmic Inflation to explain the latest Cosmic Microwave Background and Baryonic Acoustic Oscillation data is assessed by performing Bayesian model comparison within the landscape of nearly three-hundred models of single-field slow-roll inflation. We present the first Bayesian data analysis based on the third-order slow-roll primordial power spectra. In particular, the fourth Hubble-flow function ε4 remains unbounded while the third function verifies, at two-sigma, ε3 ∈[-0.4,0.5], which is perfectly compatible with the slow-roll predictions for the running of the spectral index. We also observe some residual excess of B-modes within the BICEP/Keck data favoring, at a non-statistically significant level, non-vanishing primordial tensor modes: log(ε1) > -3.9, at 68% confidence level. Then, for 287 models of single-field inflation, we compute the Bayesian evidence, the Bayesian dimensionality and the marginalized posteriors of all the models' parameters, including the ones associated with the reheating era. The average information gain on the reheating parameter R reh reaches 1.3 ± 0.18 bits, which is more than a factor two improvement compared to the first Planck data release. As such, inflationary model predictions cannot meet data accuracy without specifying, or marginalizing over, the reheating kinematics. We also find that more than 40% of the scenarios are now strongly disfavored, which shows that the constraining power of cosmological data is winning against the increase of the number of proposed models. In addition, about 20% of all models have evidences within the most probable region and are all favored according to the Jeffreys' scale of Bayesian evidences.

Toward more realistic mass functions for ultradense dark matter halos

Ultradense dark matter halos (UDMHs) are high concentrations of dark matter, assumed to have formed deep in the radiation-dominated era from amplified primordial perturbations. In this work we improve the previous works for the calculation of UDMH abundance by elaborating on the formation process of these halos by including various physical and geometrical modifications in the analysis. In particular, we investigate the impact of angular momentum, dynamical friction and triaxial collapse on the predicted mass functions for UDMHs. We perform the calculations for four primordial power spectra with different amplified features that allow for primordial black hole and UDHM formation in wide and narrow mass ranges. We also apply this analysis in the context of two possible scenarios for dark matter: the single-component and the multi-component. We find that the abundance of UDMHs is prominently enhanced in the presence of these more realistic mass functions.

Constraints on primordial curvature power spectrum with kination era: Insights from NANOGrav 15-year data set

The stochastic signal detected by the NANOGrav, PPTA, EPTA, and CPTA collaborations can be attributed to gravitational waves induced by the primordial curvature perturbations generated during inflation. These scalar-induced gravitational waves provide valuable insights into the small-scale inflation and reheating epochs. In this paper, we assume an equation of state of w=1 during reheating and adopt a log-normal form for the primordial curvature power spectrum to elucidate the observed stochastic signal. The inflation and reheating scenarios are rigorously constrained utilizing Bayesian methods applied to the NANOGrav 15-year data set. The analysis yields constraints on the reheating temperature, indicating Trh≳0.01Gev, a result consistent with constraints derived from Big Bang nucleosynthesis. Furthermore, the NANOGrav 15-year data set necessitates the primordial curvature power spectrum's amplitude and width to satisfy A∼0.01 and Δ≲0.1, respectively. Due to the change in the equation of state w, there exists a turning point in the energy density spectrum of scalar-induced gravitational waves. This suggests that if more data about the scalar-induced gravitational waves is observed, it could potentially provide constraints on the time when the reheating epoch transitions to radiation domination.

Constraints on the Primordial Curvature Power Spectrum and Reheating Temperature from the NANOGrav 15-Year Dataset

The stochastic signal observed by collaborations such as NANOGrav, PPTA, EPTA +InPTA, and CPTA may originate from gravitational waves induced by primordial curvature perturbations during inflation. This study investigates small-scale properties of inflation and reheating, assuming a log-normal form for the power spectrum of the primordial curvature and a reheating phase equation of state w=1/9. Inflation and reheating scenarios are thoroughly examined using Bayesian methods applied to the NANOGrav 15-year dataset. The analysis establishes constraints on the reheating temperature, suggesting Trh≳0.1Gev, consistent with Big Bang nucleosynthesis constraints. Additionally, the NANOGrav 15-year dataset requires the amplitude (A∼0.1) and width (Δ≲0.001) of the primordial curvature power spectrum to be within specific ranges. A notable turning point in the energy density of scalar-induced gravitational waves occurs due to a change in the equation of state w. This turning point signifies a transition from the reheating epoch to radiation domination. Further observations of scalar-induced gravitational waves could provide insights into the precise timing of this transition, enhancing our understanding of early Universe dynamics.

Quantum initial conditions for curved inflating universes

We discuss the challenges of motivating, constructing, and quantizing a canonically normalized inflationary perturbation in spatially curved universes. We show that this has historically proved challenging due to the interaction of nonadiabaticity with spatial curvature. We construct a novel curvature perturbation that is canonically normalized in the sense of its equation of motion and is unique up to a single scalar parameter. With this construction it becomes possible to set initial conditions invariant under canonical transformations, overcoming known ambiguities in the literature. This corrected quantization has potentially observational consequences via modifications to the primordial power spectrum at large angular scales, as well as theoretical implications for quantization procedures in curved cosmologies filled with a scalar field. Published by the American Physical Society 2024

Bayesian inference methodology for primordial power spectrum reconstructions from Large Scale Structure

We use Bayesian inference to develop a non-parametric method to reconstruct the primordial power spectrum Pℛ (k) from Large Scale Structure (LSS) data. The performance of the method is assessed by testing it against simulations of the clustering of high-z (QSOs) objects. Their clustering is derived from different templates of the primordial power spectrum motivated by models of inflation: the Standard Model power law characterized by the two parameters As and ns ; a local feature template; and a global oscillatory template. The primordial power spectrum is reconstructed using N knots in the log {k, Pℛ (k)} plane while sampling the cosmological parameters {H 0, Ω b , Ω c }. We use two statistical tests to examine the reconstructions for signs of primordial features: a global test comparing the evidences and a novel local test quantifying the power of the hypothesis test between the power law model and the marginalized probability over N model. We also discuss results of an application to low-z (ELGs) objects with two different photometric errors keeping the cosmology fixed. The method shows good performance in all scenarios considered. In particular, the tests show no feature detection for the standard power-law primordial power spectrum; yet, the method is able to detect power spectrum deviations at a percent level for all considered features, combining either the low-z or the high-z redshift bins. In addition, we include a test proof-of-concept application to real data from the Sloan Digital Sky Survey Luminous Red Galaxy Data Release 4 (SDSS LRG 04), finding no preference for deviations from the primordial power law. The method is flexible, model independent, and suitable for its application to existing and future LSS surveys.

Constraints on inflation with null energy condition violation from advanced LIGO and advanced Virgo's first three observing runs

The null energy condition (NEC) is a cornerstone of general relativity, and its violation could leave observable imprints in the cosmic gravitational wave spectrum. Theoretical models suggest that NEC violations during inflation can amplify the primordial tensor power spectrum, leading to distinct features in the stochastic gravitational wave background (SGWB). In this work, we search for these NEC-violating signatures in the SGWB using data from Advanced LIGO and Advanced Virgo's first three observing runs. Our analysis reveals no statistically significant evidence of such signals, allowing us to place stringent upper limits on the tensor power spectrum amplitude, P T,2, during the second inflationary stage. Specifically, we find that P T,2 ≲ 0.15 at a 95% confidence level. Notably, this upper limit is consistent with constraints derived from pulsar timing array observations, reinforcing the hypothesis that NEC violations during inflation could explain the signal detected by pulsar timing arrays. Our findings contribute to a deeper understanding of the early Universe and highlight the potential of current and future gravitational wave experiments in probing the physics of inflation and NEC violations.

Challenges to Inflation in the Post-Planck Era

Space-based missions studying the cosmic microwave background (CMB) have progressively refined the parameter space in conventional models of inflation shortly (∼10−37 s) after the Big Bang. While most inflationary scenarios proposed thus far in the context of general relativity have since been ruled out, the basic idea of inflation may still be tenable, albeit with several unresolved conundrums, such as conflicting initial conditions and inconsistencies with the measured CMB power spectrum. In the new slow-roll inflationary picture, inflation arising in plateau-like potentials requires an initiation beyond the Planck time. This delay may be consistent with the cutoff, kmin , measured recently in the primordial power spectrum. However, the actual value of kmin would imply an initiation time too far beyond the Big Bang for inflation to solve the horizon problem. In this paper, we also describe several other undesirable consequences of this delay, including an absence of well-motivated initial conditions and a significant difficulty in providing a viable mechanism for properly quantizing the primordial fluctuations. Nevertheless, many of these inconsistencies may still be avoided if one introduces nonconventional modifications to inflation, such as a brief departure from slow-roll dynamics, possibly due to a dramatic change in the inflationary potential, inflation driven by multiple fields, or a nonminimal coupling to gravity. In addition, some of these difficulties could be mitigated via the use of alternative cosmologies based, e.g., on loop quantum gravity, which replaces the initial Big Bang singularity with finite conditions at a bounce-like beginning.