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Several missions following Planck are currently under development, which will provide high-precision measurements of the Cosmic Microwave Background (CMB) anisotropies. Specifically, measurements of the E modes will become nearly limited by cosmic variance, which, especially when considering the sharpness of the E-mode transfer functions, may allow for the ability to detect deviations from the concordance model in the CMB data. We investigate the capability of upcoming missions to scrutinize models that have been proposed to address large-scale anomalies observed in the temperature spectra from WMAP and Planck. To this purpose, we consider four benchmarks that modify the CMB angular power spectra at large scales: models producing suppression, a dip, and amplification in the primordial scalar power spectrum, as well as a beyond-Lambda CDM prescription of dark energy. Our analysis shows that large-scale measurements from LiteBIRD will be able to distinguish between various types of primordial and late-time models that predict modifications to the angular spectra at these scales. Moreover, if these deviations from the standard cosmological model are determined to be systematic and do not reflect the true universe model, future experiments could potentially dismiss these features as statistical fluctuations. We also show that additional measurements from CMB-S4 can impose more stringent constraints by probing correlated signals that these models predict at smaller scales (l>100). A byproduct of our analysis is that a recently proposed "Dark Dimension" scenario, featuring power amplification at large scales, is strongly bound by current data, pushing the deviation from the standard model to unobservable scales. Overall, our results demonstrate that future CMB measurements can provide valuable insights into large-scale anomalies that are present in the current CMB data., Comment: 32 pages, 9 figures

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., Comment: 71 pages, 22 figures; v2: summary of the main results added to the introduction, matches published version

Cosmology and astrophysics provide various ways to study the properties of dark matter even if they have negligible non-gravitational interactions with the Standard Model particles and remain hidden. We study a type of hidden dark matter model in which the dark matter is completely decoupled from the Standard Model sector except gravitationally, and consists of a single species with a conserved comoving particle number. This category of hidden dark matter includes models that act as warm dark matter but is more general. In particular, in addition to having an independent temperature from the Standard Model sector, it includes cases in which dark matter is in its own thermal equilibrium or is free-streaming, obeys fermionic or bosonic statistics, and processes a chemical potential that controls the particle occupation number. While the usual parameterization using the free-streaming scale or the particle mass no longer applies, we show that all cases can be well approximated by a set of functions parameterized by only one parameter as long as the chemical potential is nonpositive: the characteristic scale factor at the time of the relativistic-to-nonrelativistic transition. We study the constraints from Big Bang Nucleosynthesis, the cosmic microwave background, the Lyman-$\alpha$ forest, and the smallest halo mass. We show that the most significant phenomenological impact is the suppression of the small-scale matter power spectrum -- a typical feature when the dark matter has a velocity dispersion or pressure at early times. So far, small dark matter halos provide the strongest constraint, limiting the transition scale factor to be no larger than $\sim1.4\times10^{-4}$ times the scale factor at matter-radiation equality., Comment: 24 pages, 3 tables, 8 figures, comments welcome

Inflationary models predicting a scale-dependent large amplification of the density perturbations have recently attracted a lot of attention because the amplified perturbations can seed a sizable amount of primordial black holes (PBHs) and stochastic background of gravitational waves (GWs). While the power spectra in these models are computed based on the linear equation of motion, it is not obvious whether loop corrections are negligible when such a large amplification occurs during inflation. In this paper, as a first step to discuss the loop corrections in such models, we use the in-in formalism and calculate the one-loop scalar power spectrum numerically and analytically in an illustrative model where the density perturbations are resonantly amplified due to oscillatory features in the inflaton potential. Our calculation is technically new in that the amplified perturbations are numerically taken into account in the in-in formalism for the first time. In arriving at our analytical estimates, we highlight the role that the Wronskian condition of perturbations, automatically satisfied in our model, plays in obtaining the correct estimates. We also discuss the necessary conditions for subdominant loop corrections in this model. We find that, for the typical parameter space leading to the $\mathcal O(10^7)$ amplification of the power spectrum required for a sufficient PBH production, the one-loop power spectrum dominates over the tree-level one, indicating the breakdown of the perturbation theory., Comment: 42 pages, 14 figures, v3: An error in the equation of the two-vertex contribution corrected. Accordingly, the splitting of the two-vertex contribution changed and Appendix B added. The final one-loop power spectrum becomes smaller than the previous results, whereas the main conclusion (the typical oscillatory models lead to dominant loop power spectra) is unchanged

Future Cosmic Microwave Background (CMB) experiments will deliver extremely accurate measurements of the E-modes pattern of the CMB polarization field. Given the sharpness of the E-modes transfer functions, such surveys make for a powerful detector of high-frequency signals from primordial features that may be lurking in current data sets. With a handful of toy models that increase the fit to the latest Planck data, but are of marginal statistical significance, we use a state-of-the-art forecast pipeline to illustrate the promising prospects to test primordial features in the next decade. Not only will future experiments allow us to detect such features in data, but they will also be able to discriminate between models and narrow down the physical mechanism originating them with high statistical significance. On the other hand, if the anomalies in the currently measured CMB spectra are just statistical fluctuations, all the current feature best fit candidates will be ruled out. Either way, our results show that primordial features are a clear target of forthcoming CMB surveys beyond the detection of tensor modes., Comment: 36 pages, 15 figures; v2 matches version published in JCAP

Features in the inflationary landscape can inject extra energies to inflation models and produce on-shell particles with masses much larger than the Hubble scale of inflation. This possibility extends the energy reach of the program of cosmological collider physics, in which signals associated with these particles are generically Boltzmann-suppressed. We study the mechanisms of this classical cosmological collider in two categories of primordial features. In the first category, the primordial feature is classical oscillation, which includes the case of coherent oscillation of a massive field and the case of oscillatory features in the inflationary potential. The second category includes any sharp feature in the inflation model. All these classical features can excite unsuppressed quantum modes of other heavy fields which leave observational signatures in primordial non-Gaussianities, including the information about the particle spectra of these heavy degrees of freedom., Comment: 49 pages, 14 figures. Changes in v2: clarifications added. Matches the version published in JCAP

The residuals of the power spectra of WMAP and Planck's cosmic microwave background (CMB) anisotropies data are known to exhibit a few interesting anomalies at different scales with marginal statistical significance. Combining bottom-up and top-down model-building approaches and using a pipeline that efficiently compares model predictions with data, we construct a model of primordial standard clock that is able to link and address the anomalies at both the large and small scales. This model, and its variant, provide some of the best fits to the feature anomalies in CMB. According to Bayes evidences, these models are currently statistically indistinguishable from the Standard Model. We show that the difference between them will soon become statistically significant with various higher quality data on the CMB polarization. We demonstrate that such a model-building and data-analyses process may be used to uncover a portion of detailed evolutionary history of our universe during its primordial epoch., Comment: 39 pages, 25 figures; v2: version published by PRD

We propose an inflationary primordial feature model that can explain both the large and small-scale anomalies in the currently measured cosmic microwave background (CMB) anisotropy spectra, revealing a clip of adventurous history of the Universe during its primordial epoch. Although the model is currently statistically indistinguishable from the Standard Model, we show that future observations such as the Simons Observatory and LiteBIRD will complement each other in distinguishing the model differences due to their accurate E-mode polarization measurements, and the PICO mission, if funded, can put stringent constraints on all characteristic properties. The model predicts a signal of classical primordial standard clock, which can also be used to distinguish the inflation and alternative scenarios in a model-independent fashion., Comment: v1: 8 pages, 4 figures; v2: consistent with the companion paper 2108.10110, main results are unaffected; v3: improved forecast analysis, version accepted by EPJC

In this paper, we use a complete model of classical primordial standard clocks as an example to develop a methodology of directly comparing numerical predictions from complicated multi-field feature models with the Planck data, including the Planck 2018 Plik unbinned likelihood and the statistically most powerful CamSpec 2020 likelihood for temperature and polarization data. As this two-field inflationary model offers a plethora of primordial feature spectra that represent combinations of sharp and resonance feature signals non-trivially distributed over extended cosmological scales, its data comparison has not been satisfactorily addressed by previous attempts using analytical templates. The method of this paper, consisting of numerical prediction, effective parameter construction and nested sampling data comparison, allows us to efficiently explore every possible spectra from the model. We classify the resulting feature candidates in three different frequency ranges. We use the Bayesian evidences to assess the statistical significance of the candidates over the baseline model, taking into account the effect of additional parameters and the look-elsewhere effect. Although none of the candidates is statistically significant, the methodology of this paper can be used to facilitate the future model-building and data-screening process of primordial features, and the candidates can be subjected to further tests with data from the upcoming cosmic microwave background polarization observations and galaxy surveys., Comment: v1: 37 pages, 19 figures and 3 tables; v2: references added, accepted for publication in JCAP

The stochastic gravitational wave background (SGWB) offers a new opportunity to observe signals of primordial features from inflationary models. We study their detectability with future space-based gravitational waves experiments, focusing our analysis on the frequency range of the LISA mission. We compute gravitational wave spectra from primordial features by exploring the parameter space of a two-field inflation model capable of generating different classes of features. Fine-tuning in scales and amplitudes is necessary for these signals to fall in the observational windows. Once they show up, several classes of frequency-dependent oscillatory signals, characteristic of different underlying inflationary physics, may be distinguished and the SGWB provides a window on dynamics of the primordial universe independent of cosmic microwave background and large-scale structure. To connect with future experimental data, we discuss two approaches of how the results may be applied to data analyses. First, we discuss the possibility of reconstructing the signal with LISA, which requires a high signal-to-noise ratio. The second more sensitive approach is to apply templates representing the spectra as estimators. For the latter purpose, we derive templates that can accurately capture the spectral features of several classes of feature signals and compare them with the SGWB produced by other physical mechanisms., Comment: 34 pages, 15 figures; v2 references added, typos corrected, accepted for publication in JCAP

Planck's residuals of the CMB temperature power spectrum present a curious oscillatory shape that resembles an extra smoothing effect of lensing and is the source of the lensing anomaly. The smoothing effect of lensing to the CMB temperature power spectrum is, to some extent, degenerate with oscillatory modulations of the primordial power spectrum, in particular if the frequency is close to that of the acoustic peaks. We consider the possibility that the lensing anomaly reported by the latest Planck 2018 results may be hinting at an oscillatory modulation generated by a massive scalar field during an alternative scenario to inflation or by a sharp feature during inflation. We use the full TTTEEE+low E CMB likelihood from Planck to derive constraints on these two types of models. We obtain that in both cases the $A_L$ anomaly is mildly reduced to slightly less than $2\sigma$, to be compared with the $2.8\sigma$ deviation from $A_L=1$ in $\Lambda$CDM. Although the oscillatory features are not able to satisfactorily ease the lensing anomaly, we find that the oscillatory modulation generated during an alternative scenario alone, i.e. with $A_L=1$, presents the lowest value of $\chi^2$, with $\Delta\chi^2=-13$ compared to $\Lambda$CDM. Furthermore, the Akaike Information Criterion suggests that such an oscillation constitutes an attractive candidate since it has a value $\Delta{\rm AIC}=-5$ with respect to $\Lambda$CDM, comparable to the $A_L$ parameter. We also obtain that the equation of state parameter in the alternative scenario is given at $1\sigma$ by $w=0.13\pm0.17$. Interestingly, the matter bounce and radiation bounce scenarios are compatible with our results. We discuss how these models of oscillatory features can be tested with future observations., Comment: revised version

Massive fields in the primordial universe function as standard clocks and imprint clock signals in the density perturbations that directly record the scale factor of the primordial universe as a function of time, a(t). A measurement of such signals would identify the specific scenario of the primordial universe in a model-independent fashion. In this Letter, we introduce a new mechanism through which quantum fluctuations of massive fields function as standard clocks. The clock signals appear as scale-dependent oscillatory signals in the power spectrum of alternative scenarios to inflation., Comment: 8 pages; v3, LSS forecast added and other minor revisions. A slightly shortened version will appear in PRL

Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition - such as in the case of smooth transition or some sharp transition scenarios - the $\mathcal{O}(1)$ local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large., Comment: 26 pages, 10 figures; v2, discussion extended and references added

Since Hubble and Lamaitre's discovery of the expanding universe using galaxies till the recent discovery of the accelerating universe using standard candles, direct measurements of the evolution of the scale factor of the universe a(t) have played central roles in establishing the standard model of cosmology. In this letter, we show that such a measurement may be extended to the primordial universe using massive fields as standard clocks, providing a direct evidence for the scenario responsible for the Big Bang. This is a short and non-technical introduction to the idea of classical and quantum primordial standard clocks., Comment: 10 pages; a short and non-technical introduction to primordial standard clocks, to appear in Science China

We introduce a generic mechanism that can extend the effects of relic anisotropies at the beginning of inflation to relatively much shorter scales in density perturbations. This is induced by non-Bunch-Davies states of the quantum fluctuations, and can show up in the non-oscillatory components of the density perturbations. This mechanism works for general forms of anisotropies, and, to illustrate it, we use an example of relic vector field. The detailed scale-dependence of these anisotropies can be used to probe the initial quantum state of our universe., Comment: 10 pages

We study the contribution of spectator massive scalar fields to the inflationary density perturbations through the universal gravitational coupling. We find that such contribution has several remarkable properties: it does not decrease as the mass of the spectator field increases; it has a significant size and cannot be turned off by any adjustable parameters; and it applies to all massive scalars existed during inflation, making the overall effect unexpectedly large. As a result, the primordial density perturbations are anomalously sensitive to the high energy physics., Comment: 4 pages

Classically oscillating massive fields can be used as "standard clocks" in the primordial universe. They generate features in primordial density perturbations that directly record the scale factor evolution a(t). Detecting and measuring these "fingerprint" signals is challenging but would provide a direct evidence for a specific primordial universe paradigm. In this paper, such a search is performed for the power spectrum of the Cosmic Microwave Background (CMB) anisotropies using the WMAP7 data. Although a good fit to the data privileges a scale around k=0.01 Mpc^(-1), we do not find statistical significance for, neither against, the presence of any feature. We then forecast the expected constraints a Planck-like CMB experiment can impose on the fingerprint parameters by using Markov-Chain-Monte-Carlo (MCMC) methods on mock data. We exhibit a high sensitivity zone for wavenumbers ranging from 0.01 Mpc^(-1) to 0.1 Mpc^(-1) in which fingerprints show up first on the posterior probability distribution of the wavenumber at which they occur, and then on the modulation frequency. Within the sensitivity zone, we show that the inflationary paradigm can be inferred from a single feature generating at least a 20% modulation of the primordial power spectrum. This minimal value sensitively depends on the modulation frequency., Comment: 22 pages, 13 figures, uses jcappub. References added, matches published version

We study the effect of massive isocurvaton on density perturbations in quasi-single field inflation models, when the mass of the isocurvaton M becomes larger than the order of the Hubble parameter H. We analytically compute the correction to the power spectrum, leading order in coupling but exact for all values of mass. This verifies the previous numerical results for the range 0

We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters., Comment: 107 pages, 14 figures, 17 tables; Inflation Working Group contribution to the CMBPol Mission Concept Study; v2: typos fixed and references added

We compute the 3-point correlation function for a general model of inflation driven by a single, minimally coupled scalar field. Our approach is based on the numerical evaluation of both the perturbation equations and the integrals which contribute to the 3-point function. Consequently, we can analyze models where the potential has a "feature", in the vicinity of which the slow roll parameters may take on large, transient values. This introduces both scale and shape dependent non-Gaussianities into the primordial perturbations. As an example of our methodology, we examine the ``step'' potentials which have been invoked to improve the fit to the glitch in the $$ $C_l$ for $l \sim 30$, present in both the one and three year WMAP data sets. We show that for the typical parameter values, the non-Gaussianities associated with the step are far larger than those in standard slow roll inflation, and may even be within reach of a next generation CMB experiment such as Planck. More generally, we use this example to explain that while adding features to potential can improve the fit to the 2-point function, these are generically associated with a greatly enhanced signal at the 3-point level. Moreover, this 3-point signal will have a very nontrivial shape and scale dependence, which is correlated with the form of the 2-point function, and may thus lead to a consistency check on the models of inflation with non-smooth potentials., Comment: 23 pages JHEP-style, 7 Figures. Updated with improved results. Accepted for publication by JCAP