We apply in a simple model derived from quadratic <math altimg='si2.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math> gravity the technique of Dyson-Schwinger equations to solve for its corresponding quantum theory. Particularly, we solve the classical equations of motion to get a solution to the hierarchy of Dyson-Schwinger equations in the limit of large Ricci scalar, assumed to be constant and larger than the square of the Starobinsky mass. Moving to the Einstein frame, the model admits Higgs-like solutions with a single particle having a finite mass. We quantize the scalar field showing the appearing of a mass gap through a Higgs-like solution. The presence of the mass gap, that increases with the square root of the Ricci scalar, shows how the effect of the scalar sector at low-energy becomes ineffective, making it relevant only at short distances.

India

Sayantan Choudhury

Italy

Marco Frasca

Poland

Anish Ghoshal

Mass gap in non-perturbative quadratic <math altimg='si2.svg'><msup><mi mathvariant='script'>R</mi><mn>2</mn></msup></math> gravity via Dyson-Schwinger

Non-Gaussianity in the primordial curvature perturbation is a crucial element of the early universe due to its significant impact on the primordial black hole (PBH) production. In this work, we focus on the effects of negative non-Gaussianity on PBH abundance through the lens of the compaction function criterion for PBH formation. Our setup utilizes an effective field theory of non-singular bounce, including the standard slow-roll inflation with an ultra-slow roll phase for amplifying the curvature perturbations to form PBHs. We investigate with two separate values of the non-Gaussianity parameter, $$f_\textrm{NL}=(-\,39.95,-\,35/8)$$ , found within the ekpyrotic contraction and the matter bounce scenarios, respectively, and show that a negatively large amount of $$f_\textrm{NL}$$ can provide sizeable abundance, $$10^{-3}\leqslant f_\textrm{PBH}\leqslant 1$$ , and completely mitigates the PBH overproduction issue. We also highlight that the case with the effective sound speed $$c_{s}=1$$ , coupled with $$f_\textrm{NL}=-\,39.95$$ , provides an agreement under $$1\sigma $$ for the scalar-induced gravitational wave explanation of the latest PTA (NANOGrav15 and EPTA) signal. Lastly, we extract an upper bound on the most negative value of, $$f_\textrm{NL}\sim -60$$ , below which we show breaching of the underlying perturbativity constraints on the power spectrum amplitude.

Kritartha Dey

Siddhant Ganguly

Ahaskar Karde

Swapnil Kumar Singh

Pranjal Tiwari

Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce

We present a study of the Effective Field Theory (EFT) generalization of stochastic inflation in a model-independent single-field framework and its impact on primordial black hole (PBH) formation. We show how the Langevin equations for the “soft” modes in quasi de Sitter background is described by the Infra-Red (IR) contributions of scalar perturbations, and the subsequent Fokker–Planck equation driving the probability distribution for the stochastic duration $$\mathcal {N}$$ , significantly modify in the present EFT picture. An explicit perturbative analysis of the distribution function by implementing the stochastic- $$\delta N$$ formalism is performed up to the next-to-next-to-next-to-leading order (NNNLO) for both the classical-drift and quantum-diffusion dominated regimes. In the drift-dominated limit, we perturbatively analyse the local non-Gaussianity parameters $$(f_\textrm{NL}, g_\textrm{NL}, \tau _\textrm{NL})$$ with the EFT-induced modifications. In the diffusion-dominated limit, we numerically compute the probability distribution featuring exponential tails at each order of perturbative treatment.

Pankaj Padiyar

Kazakhstan

China

M. Sami

Primordial black holes from effective field theory of stochastic single field inflation at NNNLO

We present a complete and consistent exposition of the regularization, renormalization, and resummation procedures in the setup of having a contraction and then non-singular bounce followed by inflation with a sharp transition from slow-roll (SR) to ultra-slow roll (USR) phase for generating primordial black holes (PBHs). We consider following an effective field theory (EFT) approach and study the quantum loop corrections to the power spectrum from each phase. We demonstrate the complete removal of quadratic UV divergences after renormalization and softened logarithmic IR divergences after resummation and illustrate the scheme-independent nature of our renormalization approach. We further show that the addition of a contracting and bouncing phase allows us to successfully generate PBHs of solar-mass order,  $$M_\textrm{PBH}\sim \mathcal{O}(M_{\odot })$$  <math> <mrow> <msub> <mi>M</mi> <mtext>PBH</mtext> </msub> <mo>∼</mo> <mi>O</mi> <mrow> <mo>(</mo> <msub> <mi>M</mi> <mo>⊙</mo> </msub> <mo>)</mo> </mrow> </mrow> </math>  , by achieving the minimum e-folds during inflation to be  $$\Delta N_{\textrm{Total}}\sim \mathcal{O}(60)$$  <math> <mrow> <mi>Δ</mi> <msub> <mi>N</mi> <mtext>Total</mtext> </msub> <mo>∼</mo> <mi>O</mi> <mrow> <mo>(</mo> <mn>60</mn> <mo>)</mo> </mrow> </mrow> </math>   and in this process successfully evading the strict no-go theorem. We notice that varying the effective sound speed between  $$0.88\leqslant c_{s}\leqslant 1$$  <math> <mrow> <mn>0.88</mn> <mo>⩽</mo> <msub> <mi>c</mi> <mi>s</mi> </msub> <mo>⩽</mo> <mn>1</mn> </mrow> </math>  , allows the peak spectrum amplitude to lie within  $$10^{-3}\leqslant A \leqslant 10^{-2}$$  <math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> <mo>⩽</mo> <mi>A</mi> <mo>⩽</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math>  , indicating that causality and unitarity remain protected in the theory. We analyse PBHs in the extremely small,  $$M_{\textrm{PBH}}\sim \mathcal{O}(10^{-33}-10^{-27})M_{\odot }$$  <math> <mrow> <msub> <mi>M</mi> <mtext>PBH</mtext> </msub> <mo>∼</mo> <mi>O</mi> <mrow> <mo>(</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>33</mn> </mrow> </msup> <mo>-</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>27</mn> </mrow> </msup> <mo>)</mo> </mrow> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>  , and the large,  $$M_{\textrm{PBH}}\sim \mathcal{O}(10^{-6}-10^{-1})M_{\odot }$$  <math> <mrow> <msub> <mi>M</mi> <mtext>PBH</mtext> </msub> <mo>∼</mo> <mi>O</mi> <mrow> <mo>(</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> <mo>-</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>  , mass limits and confront the PBH abundance results with the latest microlensing constraints. We also study the cosmological beta functions across all phases and find their interpretation consistent in the context of bouncing and inflationary scenarios while satisfying the pivot scale normalization requirement. Further, we estimate the spectral distortion effects and shed light on controlling PBH overproduction.

Sudhakar Panda

Soumitra SenGupta

Regularized-renormalized-resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation

We consider the production of secondary gravity waves in Galileon inflation with an ultra-slow roll (USR) phase and show that the spectrum of scalar-induced gravitational waves (SIGWs) in this case is consistent with the recent NANOGrav 15-year data and with sensitivities of other ground and space-based missions, LISA, BBO, DECIGO, CE, ET, HLVK (consists of aLIGO, aVirgo, and KAGRA), and HLV(03). Thanks to the non-renormalization property of Galileon theory, the amplitude of the large fluctuation is controllable at the sharp transitions between SR and USR regions. We show that the behavior of the GW spectrum, when one-loop effects are included in the scalar power spectrum, is preserved under a shift of the sharp transition scale with peak amplitude <math><msub><mrow><mi>Ω</mi></mrow><mrow><mi>GW</mi></mrow></msub><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>∼</mo><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup><mo>)</mo></math>, and hence it can cover a wide range of frequencies within <math><mi>O</mi><mo>(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup><mspace width="0.25em"></mspace><mrow><mi>Hz</mi></mrow><mo>−</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>7</mn></mrow></msup><mspace width="0.25em"></mspace><mrow><mi>Hz</mi></mrow><mo>)</mo></math>. An analysis of the allowed mass range for primordial black holes (PBHs) is also performed, where we find that mass values ranging from <math><mi>O</mi><mo>(</mo><mn>1</mn><msub><mrow><mi>M</mi></mrow><mrow><mo>⊙</mo></mrow></msub><mo>−</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>18</mn></mrow></msup><msub><mrow><mi>M</mi></mrow><mrow><mo>⊙</mo></mrow></msub><mo>)</mo></math> can be generated over the corresponding allowed range of low and high frequencies.

Scalar induced gravity waves from ultra slow-roll galileon inflation

We examine the possibility of Primordial Black Holes (PBHs) formation in single field models of inflation. Using the adiabatic or wave function renormalization scheme in the short range modes, we show that one-loop correction to the power spectrum is free from quadratic UV divergence. We consider a framework in which PBHs are produced during the transition from Slow Roll (SR) to Ultra Slow Roll (USR) followed by the end of inflation. We demonstrate that the renormalized power spectrum soften the contribution of the logarithmic IR divergence and severely restricts the possible mass range of produced PBHs in the said transition, namely,  $$M_\textrm{PBH}\sim 10^{2}\,\textrm{g}$$  <math> <mrow> <msub> <mi>M</mi> <mtext>PBH</mtext> </msub> <mo>∼</mo> <msup> <mn>10</mn> <mn>2</mn> </msup> <mspace width="0.166667em"></mspace> <mtext>g</mtext> </mrow> </math>    $$\hat{\textrm{a}}$$  <math> <mover> <mtext>a</mtext> <mo>^</mo> </mover> </math>   la a no-go theorem. In particular, we find that the produced PBHs are short lived ( $$t^\textrm{evap}_\textrm{PBH}\sim 10^{-20}\,\textrm{s}$$  <math> <mrow> <msubsup> <mi>t</mi> <mtext>PBH</mtext> <mtext>evap</mtext> </msubsup> <mo>∼</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>20</mn> </mrow> </msup> <mspace width="0.166667em"></mspace> <mtext>s</mtext> </mrow> </math>  ) and the corresponding number of e-folds in the USR region is restricted to  $$\Delta {\mathcal {N}}_\textrm{USR}\approx 2$$  <math> <mrow> <mi>Δ</mi> <msub> <mi>N</mi> <mtext>USR</mtext> </msub> <mo>≈</mo> <mn>2</mn> </mrow> </math>  .

Mayukh Gangopadhyay

No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation

We investigate the explicit role of negative local non-Gaussianity, <math><msub><mrow><mi>f</mi></mrow><mrow><mi>NL</mi></mrow></msub></math>, in suppressing the abundance of primordial black holes (PBHs) in the single-field model of Galileon inflation. PBH formation requires significantly enhancing the scalar power spectrum, which greatly affects their abundance. The associated frequencies in the nHz regime are also sensitive to the generation of scalar-induced gravitational waves (SIGWs) which may explain the current data from the pulsar timing arrays (PTAs). Our analysis using the threshold statistics on the compaction function demonstrates that Galileon theory not only avoids PBH overproduction using the curvature perturbation enhancements that give <math><msub><mrow><mi>f</mi></mrow><mrow><mi>NL</mi></mrow></msub><mo>∼</mo><mi>O</mi><mo>(</mo><mo>−</mo><mn>6</mn><mo>)</mo></math>, but also generates SIGWs that conform well with the PTA data.

Primordial non-Gaussianity as a saviour for PBH overproduction in SIGWs generated by pulsar timing arrays for Galileon inflation

In this work, we present a quintessential interpretation of having a blue-tilted tensor power spectrum for canonical single-field slow-roll inflation to explain the recently observed Pulsar Timing Array (NANOGrav 15-year and EPTA) signal of Gravitational Waves (GW). We formulate the complete semi-classical description of cosmological perturbation theory in terms of scalar and tensor modes using the Non-Bunch Davies initial condition. We found that the existence of the blue tilt  $$(n_t)$$  <math> <mrow> <mo>(</mo> <msub> <mi>n</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> </math>   within the favoured range  $$1.2&lt;n_t&lt;2.5$$  <math> <mrow> <mn>1.2</mn> <mo>&lt;</mo> <msub> <mi>n</mi> <mi>t</mi> </msub> <mo>&lt;</mo> <mn>2.5</mn> </mrow> </math>   can be explained in terms of a newly derived consistency relation. Further, we compute a new field excursion formula using the Non-Bunch Davies initial condition, that validates the requirement of Effective Field Theory in the sub-Planckian regime,  $$|\Delta \phi |\ll M_{\textrm{pl}}$$  <math> <mrow> <mrow> <mo>|</mo> <mi>Δ</mi> <mi>ϕ</mi> <mo>|</mo> </mrow> <mo>≪</mo> <msub> <mi>M</mi> <mtext>pl</mtext> </msub> </mrow> </math>   for the allowed value of the tensor-to-scalar ratio,  $$r&lt;0.06$$  <math> <mrow> <mi>r</mi> <mo>&lt;</mo> <mn>0.06</mn> </mrow> </math>   from CMB observations. In our study, we refer to this result as Anti Lyth bound as it violates the well-known Lyth bound originally derived for Bunch Davies initial condition. Further, we study the behaviour of the spectral density of GW and the associated abundance with the frequency, which shows that within the frequency domain  $$10^{-9}~{\textrm{Hz}}&lt;f&lt;10^{-7}~{\textrm{Hz}}$$  <math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>9</mn> </mrow> </msup> <mspace width="3.33333pt"></mspace> <mtext>Hz</mtext> <mo>&lt;</mo> <mi>f</mi> <mo>&lt;</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> <mspace width="3.33333pt"></mspace> <mtext>Hz</mtext> </mrow> </math>   the outcome obtained from our analysis is completely consistent with the Pulsar Timing Array (NANOGrav 15-year and EPTA) signal. Also, we found that the behaviour of GW spectra satisfies the CMB constraints at the low frequency,  $$f_*\sim 7.7\times 10^{-17}~{\textrm{Hz}}$$  <math> <mrow> <msub> <mi>f</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msub> <mo>∼</mo> <mn>7.7</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>17</mn> </mrow> </msup> <mspace width="3.33333pt"></mspace> <mtext>Hz</mtext> </mrow> </math>   corresponding to the pivots scale wave number,  $$k_*\sim 0.05~{\textrm{Mpc}}^{-1}.$$  <math> <mrow> <msub> <mi>k</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msub> <mo>∼</mo> <mn>0.05</mn> <mspace width="3.33333pt"></mspace> <msup> <mrow> <mtext>Mpc</mtext> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>.</mo> </mrow> </math>   Finally, the sharp falling behaviour of the GW spectra within the frequency domain  $$10^{-7}~{\textrm{Hz}}&lt;f&lt;1~{\textrm{Hz}}$$  <math> <mrow> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>7</mn> </mrow> </msup> <mspace width="3.33333pt"></mspace> <mtext>Hz</mtext> <mo>&lt;</mo> <mi>f</mi> <mo>&lt;</mo> <mn>1</mn> <mspace width="3.33333pt"></mspace> <mtext>Hz</mtext> </mrow> </math>   validates our theory in the comparatively high-frequency regime as well.

Single field inflation in the light of Pulsar Timing Array Data: quintessential interpretation of blue tilted tensor spectrum through Non-Bunch Davies initial condition

In this article, we study the quantum field theoretic generalization of the Caldeira-Leggett model in general curved space-time considering interactions between two scalar fields in a classical gravitational background. The thermalization phenomena is then studied from the obtained de Sitter solution using quantum quench from one scalar field model obtained from path integrated effective action. We consider an instantaneous quench in the time-dependent mass protocol of the field of our interest. We find that the dynamics of the field post-quench can be described in terms of the state of the generalized Calabrese-Cardy (gCC) form and computed the different types of two-point correlation functions in this context. We explicitly found the conserved charges of <math><msub><mrow><mi>W</mi></mrow><mrow><mo>∞</mo></mrow></msub></math> algebra that represents the gCC state after a quench in de Sitter space and found it to be significantly different from the flat space-time results. We extend our study for the different two-point correlation functions not only considering the pre-quench state as the ground state, but also a squeezed state. We found that irrespective of the pre-quench state, the post quench state can be written in terms of the gCC state showing that the subsystem of our interest thermalizes in de Sitter space. Furthermore, we provide a general expression for the two-point correlators and explicitly show the thermalization process by considering a thermal Generalized Gibbs ensemble (GGE). Finally, from the equal time momentum dependent counterpart of the obtained results for the two-point correlators, we have studied the hidden features of the power spectra and studied its consequences for different choices of the quantum initial conditions.

Subhashish Banerjee

Satyaki Chowdhury

Germany

Johannes Knaute

K. Shirish

Thermalization in quenched open quantum cosmology

Using the Effective Field Theory (EFT) framework of single field inflation, we investigate the possibility of the formation of Primordial Black Holes (PBHs) in the Slow Roll (SR) to Ultra Slow Roll (USR) sharp transition. We demonstrate that, due to one-loop correction to the power spectrum, causality is violated (<math><msub><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>&gt;</mo><mn>1</mn></math>) for the mass range of PBHs, <math><msub><mrow><mi>M</mi></mrow><mrow><mi>PBH</mi></mrow></msub><mo>&gt;</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>2</mn></mrow></msup><mrow><mi>gm</mi></mrow></math> created during the said transition. We find that non-canonical features with <math><msub><mrow><mi>c</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>&lt;</mo><mn>1</mn></math> worsen the predictions of the canonical framework of single-field inflation.