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.

China

Shi Pan

Yong Cai

Yun-Song Piao

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

We investigate the parity-violating effects in primordial gravitational waves (GWs) due to null energy condition (NEC) violation in two very early universe scenarios: bounce-inflation and intermediate NEC violation during inflation. In both scenarios, we numerically solve the power spectra of parity-violating primordial GWs generated by coupling the background field and the spectator field with the Nieh-Yan term, respectively. We find that the background field can significantly enhance parity-violating effects at scales corresponding to the maximum of the GW power spectra. In contrast, the parity-violating effects produced by the spectator show significantly weaker observability even if the coupling constant is large. Therefore, in NEC-violating scenarios, the significant observable parity-violating effects in primordial GWs primarily arise from the physics directly related to NEC violation. This result highlights the potential of primordial GWs as crucial tools for exploring NEC-violating and parity-violating physics.

Zi-Wei Jiang

Fei Wang

Parity-violating primordial gravitational waves from null energy condition violation

Recently, evidence of stochastic gravitational wave background (SGWB) signals observed by pulsar timing array (PTA) collaborations, has prompted investigations into their origins. We explore the compatibility of a proposed inflationary scenario, incorporating an intermediate null energy condition (NEC)-violating phase, with the PTA observations. The NEC violation potentially amplifies the primordial tensor power spectrum, offering a promising explanation for PTA observations. Numerical analyses, primarily focused on NANOGrav’s 15-year results, reveal the model’s compatibility with PTA data. Notably, the model predicts a nearly scale-invariant GW spectrum in the mHz frequency range, which sets our scenario apart from other interpretations predicting a red primordial GW spectrum on smaller scales.

Netherlands

Gen Ye

Poland

Mian Zhu

Null energy condition violation during inflation and pulsar timing array observations

Recent pulsar timing array (PTA) experiments have reported strong evidence of the stochastic gravitational wave background (SGWB). If interpreted as primordial gravitational waves (GWs), the signal favors a strongly blue-tilted spectrum. Consequently, the nonsingular cosmology, which is able to predict a strongly blue-tilted GW spectrum with  $$n_T \simeq 2$$  <math> <mrow> <msub> <mi>n</mi> <mi>T</mi> </msub> <mo>≃</mo> <mn>2</mn> </mrow> </math>   on certain scales, offers a potential explanation for the observed SGWB signal. In this paper, we present a Genesis-inflation model capable of explaining the SGWB signal observed by the PTA collaborations while also overcoming the initial singularity problem associated with the inflationary cosmology. Furthermore, our model predicts distinctive features in the SGWB spectrum, which might be examined by forthcoming space-based gravitational wave experiments.

Pulsar timing array observations as possible hints for nonsingular cosmology

We investigate the possibility of the enhancement of parity-violation signal in bouncing cosmology. Specifically, we are interested in deciding which phase should generate the most significant parity-violation signals. We find that the dominant contribution comes from the bouncing phase, while the contraction phase has a smaller contribution. Therefore, bouncing cosmology can enhance the parity-violation signals during the bouncing phase. Moreover, since the bouncing phase has the highest energy scale in bouncing cosmology, we can also probe new physics at this scale by studying the parity-violation effect.

Parity-violation in bouncing cosmology

Ji Xu

United States

Shuai Zhao

Japan

Siyi Zhou

Erratum to: Perturbative unitarity and NEC violation in genesis cosmology

Explorations of the violation of null energy condition (NEC) in cosmology could enrich our understanding of the very early universe and the related gravity theories. Although a fully stable NEC violation can be realized in the “beyond Horndeski” theory, it remains an open question whether a violation of the NEC is allowed by some fundamental properties of UV-complete theories or the consistency requirements of effective field theory (EFT). We investigate the tree-level perturbative unitarity for stable NEC violations in the contexts of both Galileon and “beyond Horndeski” genesis cosmology, in which the universe is asymptotically Minkowskian in the past. We find that the constraints of perturbative unitarity imply that we may need some unknown new physics below the cut-off scale of the EFT other than that represented by the “beyond Horndeski” operators.

Perturbative unitarity and NEC violation in genesis cosmology

We investigate both the null energy condition (NEC) violating scenario and the c  T -diminishing scenario for generating enhanced power spectrum of primordial gravitational waves (GWs) during inflation, where c  T  is the propagating speed of primordial GWs. Both of these two scenarios can be realized stably with theories beyond Horndeski, hence can be uniformly implemented within the framework of the effective field theory. We calculate the power spectrum of primordial GWs by assuming that the inflationary Universe undergoes three phases, where the violation of NEC or the diminishment of c  T  occurs in the intermediate phase. A template of the spectrum is given for the NEC-violating scenario. We also discuss the underlying relation and discrepancy between these two scenarios with a disformal transformation.

Generating enhanced primordial GWs during inflation with intermittent violation of NEC and diminishment of GW propagating speed

It is well-known that the first-order phase transition (PT) will yield a stochastic gravitational waves (GWs) background with a peculiar spectrum. However, we show that when such a PT happened during the primordial inflation, the GWs spectrum brought by the PT will be reddened, which thus records the unique voiceprint of inflation. We assess the abilities of the GW detectors to detect the corresponding signal.

Yu-Tong Wang

Phase-transition sound of inflation at gravitational waves detectors

The theory of perturbative reheating in the Sneutrino-Higgs cosmology of the B-L MSSM is presented. It is shown that following an epoch of inflation consistent with all Planck2015 data, the inflaton begins to oscillate around its minimum at zero and to reheat to various species of standard model and supersymmetric matter. The perturbative decay rates to this matter are computed, both analytically and numerically. Using these results, the Hubble parameter and the relative energy densities for each matter species, including that of the inflaton, are calculated numerically. The inflaton energy density is demonstrated to vanish at an energy scale of  <math><mi>O</mi></math> $$ \mathcal{O} $$(1013) GeV, signaling the end of the period of reheating. The newly created matter background is shown to be in thermal equilibrium, with a reheating temperature of ≃ 1.13 × 1013 GeV. To allow for a B-L breaking scale sufficiently smaller than the reheating scale, we extend the statistical method of determining the soft supersymmetry breaking parameters developed in previous work. The result is that one can determine a large number of phenomenologically realistic initial conditions for which the B-L breaking scale is an order of magnitude or more smaller than the reheating scale.