We study the inflationary scenario in the Tsallis entropy-based cosmology. The Friedmann equations in this setup can be derived by using the first law of thermodynamics. To derive the relations of the power spectra of the scalar and tensor perturbations in this setup, we reconstruct an f(R) gravity model which is thermodynamically equivalent to our model in the slow-roll approximation. In this way, we find the inflationary observables, including the scalar spectral index and the tensor-to-scalar ratio in our scenario. Then, we investigate two different potentials in our scenario, including the quadratic potential and the potential associated with the natural inflation in which the inflaton is an axion or a pseudo-Nambu–Goldstone boson. We examine their observational viability in light of the Planck 2018 CMB data. We show that although the results of these potentials are in tension with the observations in the standard inflationary setting, their consistency with the observations can be significantly improved within the setup of the Tsallis entropy-based inflation. Moreover, we place constraints on the parameters of the considered inflationary models by using the current observational data.

Iran

Zeinab Teimoori

Kazem Rezazadeh

Abasat Rostami

Inflation based on the Tsallis entropy

Releasing the 12.5-year pulsar timing array data, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported the evidence for a stochastic common-spectrum which would herald the detection of a stochastic gravitational wave background (SGWB) for the first time. We investigate if the signal could be generated from the end of a ∼10 MeV but still phenomenologically viable double-field inflation when the field configuration settles to its true vacuum. During the double-field inflation at such scales, bubbles of true vacuum that can collapse to LIGO mass, and heavier primordial black holes form. We show that only when this process happens with a first-order phase transition, the produced gravitational wave spectrum can match with the NANOGrav acclaimed SGWB signal. We show that the produced gravitational wave spectrum matches the NANOGrav SGWB signal only when this process happens through a first-order phase transition. Using LATTICEEASY, we also examine the previous observation in the literature that by lowering the scale of preheating, despite the shift of the peak frequency of the gravitational wave profile to smaller values, the amplitude of the SGWB could be kept almost constant. We notice that this observation breaks down at the preheating scale, <math><mi>M</mi><mo>≲</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>14</mn></mrow></msup><mspace width="0.25em"></mspace><msub><mrow><mi>m</mi></mrow><mrow><msub><mrow></mrow><mrow><mi>Pl</mi></mrow></msub></mrow></msub></math>.

Amjad Ashoorioon

Abasalt Rostami

NANOGrav signal from the end of inflation and the LIGO mass and heavier primordial black holes

We study the non-Gaussianity and secondary Gravitational Waves (GWs) in the process of the Primordial Black Holes (PBHs) production from inflation. In our work, we focus on the  $$\alpha $$  <math> <mi>α</mi> </math>  -attractor inflation model in which a tiny bump in the inflaton potential enhances the amplitude of the curvature perturbations at some scales and consequently leads to the PBHs production with different mass scales. We implement the computational code BINGO which calculates the non-Gaussianity parameter in different triangle configurations. Our examination implies that in this setup, the non-Gaussianity gets amplified significantly in the equilateral shape around the scales in which the power spectrum of the scalar perturbations undergoes a sharp declination. The imprints of these non-Gaussianities can be probed in the scales corresponding to the BBN and  $$\mu $$  <math> <mi>μ</mi> </math>  -distortion events, or in smaller scales, and detection of such signatures in the future observations may confirm the idea of our model for the generation of PBHs or rule it out. Moreover, we investigate the secondary GWs in this framework and show that in our model, the peak of the present fractional energy density is obtained as  $$\Omega _{\mathrm{GW0}} \sim 10^{-8}$$  <math> <mrow> <msub> <mi>Ω</mi> <mrow> <mi>GW</mi> <mn>0</mn> </mrow> </msub> <mo>∼</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>8</mn> </mrow> </msup> </mrow> </math>   at different frequencies which depends on the model parameters. These results lie well within the sensitivity region of some GWs detectors at some frequencies, and therefore the observational compatibility of our model can be evaluated by the forthcoming data from these detectors. We further provide some estimations for the tilts of the induced GWs spectrum in the different intervals of frequency, and demonstrate that the spectrum obeys the power-law relation  $$\Omega _{\mathrm{GW0}}\sim f^{n}$$  <math> <mrow> <msub> <mi>Ω</mi> <mrow> <mi>GW</mi> <mn>0</mn> </mrow> </msub> <mo>∼</mo> <msup> <mi>f</mi> <mi>n</mi> </msup> </mrow> </math>   in those frequency bands.

Saeid Karimi

Kayoomars Karami

Non-Gaussianity and secondary gravitational waves from primordial black holes production in  $$\alpha $$  <math> <mi>α</mi> </math>  -attractor inflation

We show how in a matrix inflationary model in which there is a non-minimal coupling between the matrix inflatons and gravity — hence dubbed Non-M-flation — some of the disadvantages of the minimal model can be avoided. In particular, the number of D3 branes can be reduced substantially to   <math> <munder> <mo>&lt;</mo> <mo>∼</mo> </munder> <mi>O</mi> <mfenced> <mn>100</mn> </mfenced> </math>  $$ \underset{\sim }{&lt;}\mathcal{O}(100) $$ , which can alleviate the “potential” backreaction problem of large number of D3 branes on the background geometry. This is achieved by values of non-minimal coupling of order few hundred, which is much smaller than that of Higgs Inflation. The prediction of the model in the symmetry breaking part of the potential, which is a local attractor and can support eternal inflation, is compatible with the latest PLANCK results. In contrast to the minimal model, the spectator fields can partially or completely reheat the universe, depending on the symmetry-breaking vacuum expectation value and the non-minimal coupling parameter. We also comment on how the presence of gauge species keep the UV cutoff at around the Planck scale in the Einstein frame and, in contrast to the Higgs inflation, the problem of field displacements beyond the cutoff does not occur.