Search Results (11)

The de-Sitter spacetime is a maximally symmetric Lorentzian manifold with constant positive scalar curvature that plays a fundamental role in modern cosmology. Here, we investigate bulk-viscosity-assisted quasi de-Sitter inflation, that is the period of accelerated expansion in the early universe during which $-\dot{H}\ll H^2$, with $H\left(t\right)$ being the Hubble expansion rate. We do so in the framework of a causal theory of relativistic hydrodynamics, which takes into account non-equilibrium effects associated with bulk viscosity, which may have been present as the early universe underwent an accelerated expansion. In this framework, the existence of a quasi de-Sitter universe emerges as a natural consequence of the presence of bulk viscosity, without requiring introducing additional scalar fields. As a result, the equation of state, determined by numerically solving the generalized momentum-conservation equation involving bulk viscosity pressure turns out to be time dependent. The transition timescale characterising its departure from an exact de-Sitter phase is intricately related to the magnitude of the bulk viscosity. We examine the properties of the new equation of state, as well as the transition timescale in the presence of bulk viscosity pressure. In addition, we construct a fluid description of inflation and demonstrate that, in the context of the causal formalism, it is equivalent to the scalar field theory of inflation. Our analysis also shows that the slow-roll conditions are realised in the bulk-viscosity-supported model of inflation. Finally, we examine the viability of our model by computing the inflationary observables, namely the spectral index and the tensor-to-scalar ratio of the curvature perturbations, and compare them with a number of different observations, finding good agreement in most cases. Full article

A crucial material comprising a pneumatic tire is rubber. In general, the tire, or more specifically, the hysteresis effects brought on by the deformation of the part made of rubber during the procedure, heat up the part. In addition, the tire temperature depends on several factors, including the inflation pressure, automobile loading, car speed, road tire, the environmental conditions, and the tire geometry. This work focuses on using simulations to calculate the temperature and generated heat flow distributions of a rolling tire with constant velocity using the finite element method. For the sake of simplicity, it is assumed that the only components of the tire are rubber, body-ply, bead wire, and the rim. While the other components are believed to be made of a linear elastic material, the nonlinear mechanical behavior of the rubber is characterized by a Mooney–Rivlin model. Investigations are conducted into the combined effects of vehicle loads and inflation pressure. Hysteresis energy loss is used as a bridge to link the strain energy density to the heat source in rolling tires, and their temperature and heat flow distributions may be determined by steady-state thermal analysis. Thanks to the state-of-the-art computing method, the time required for connected 3D dynamic rolling tire simulations is reduced. The simulation outcomes demonstrate that the maximum temperature in this paper is attained with high weights, high velocities, and low inner inflated pressures. Overall, the maximum temperature is increased with the rise of all three variables. Moreover, the rise of the friction coefficient between the tread and road surface moves the high-temperature area towards the tread/sidewall connection area. Full article

Single field inflationary models are investigated within Palatini quadratic gravity, represented by $R+\alpha R^2$, along with a non-minimal coupling of the form $f\left(\varphi \right)R$ between the inflaton field $\varphi$ and the gravity. The treatment is performed in the Einstein frame, where the minimal coupling to gravity is recovered through conformal transformation. We consider various limits of the model with different inflationary scenarios characterized as canonical slow-roll inflation in the limit $\alpha {\dot{\varphi }}^2\ll (1+f\left(\varphi \right))$, constant-roll k-inflation for $\alpha \ll 1$, and slow-roll K-inflation for $\alpha \gg 1$. A cosine and exponential potential are examined with the limits mentioned above and different well-motivated non-minimal couplings to gravity. We compare the theoretical results, exemplified by the tensor-to-scalar r ratio and spectral index $n_s$, with the recent observational results of Planck 2018 and BICEP/Keck. Furthermore, we include the results of a new study forecast precision with which $n_s$ and r can be constrained by currently envisaged observations, including CMB (Simons Observatory, CMB-S4, and LiteBIRD). Full article

We study the constant-roll tachyon inflation with large and small $\eta$. In previous studies, only the constant-roll tachyon inflation with small $\eta$ is consistent with the observations. We find that the duality between the constant-roll tachyon inflation with large and small $\eta$ may exist. The apparent duality suggests that the constant-roll tachyon inflationary model with large $\eta$ may also be consistent with the observations. By fitting the spectral tilde $n_s$ and tensor to scalar ratio r, which is a measure of primordial gravitational waves with the observations, we get small and large $\eta$ in this range $-0.01629\le {\eta }_H\le -0.00079$ and $3.00081\le {\eta }_H\le 3.01621$ at the 2$\sigma$ C.L for $N=60$ efolds. Full article

In this paper, we study the inflationary scenario in logarithmic $f\left(R\right)$ gravity, where the rate of inflation roll is constant. On the other hand, our gravitational $f\left(R\right)$ model is a polynomial plus a logarithmic term. We take advantage of constant-roll conditions and investigate the cosmic evolution of the logarithmic $f\left(R\right)$ gravity. We present a numerical and a graphical study using the model parameters. Additionally, we obtain the corresponding potential by using the constant-roll condition. We obtain the exact value of the potential satisfying the constant-roll conditions. Next, we challenge it with refined swampland conjecture with respect to the Planck data. Finally, we compare our results with the latest observable data. Full article

We show that upon applying Palatini $f\left(R\right)$, characterized by an $\alpha R^2$ term, within a scenario motivated by a temporal variation of strong coupling constant, then one obtains a quadratic kinetic energy. We do not drop this term, but rather study two extreme cases: $\alpha <<1$ and $\alpha >>1$. In both cases, one can generate a kinematically-induced inflationary paradigm. In order to fit the Planck 2018 data, the $\alpha >>1$ case, called k-inflation, requires a fine tuning adjustment with nonvanishing nonminimal coupling to gravity parameter $\xi$, whereas the $\alpha <<1$ case, studied in the constant-roll regime, can fit the data for vanishing $\xi$. The varying strong coupling inflation scenario remains viable when implemented through a warm inflation scenario with or without $f\left(R\right)$ gravity. Full article

We review the recently proposed Trans-Planckian Censorship Conjecture (TCC) that stems from the trans-Planckian problem of cosmological perturbations. We analyze the implications and constraints that the TCC introduces in different frameworks of viable inflation. We revisit the case of slow-roll scalar field inflation and we investigate the cases of slow-roll $f\left(R\right)$ and $f(R,\varphi )$-gravity. Finally, we consider the conjecture in the context of constant-roll scalar field inflation. Full article

The time-dependent cosmological term arises from the energy-momentum tensor calculated in a state different from the ground state. We discuss the expectation value of the energy-momentum tensor on the right hand side of Einstein equations in various (approximate) quantum pure as well as mixed states. We apply the classical slow-roll field evolution as well as the Starobinsky and warm inflation stochastic equations in order to calculate the expectation value. We show that, in the state concentrated at the local maximum of the double-well potential, the expectation value is decreasing exponentially. We confirm the descent of the expectation value in the stochastic inflation model. We calculate the cosmological constant Λ at large time as the expectation value of the energy density with respect to the stationary probability distribution. We show that $\Lambda \simeq {\gamma }^{\frac{4}{3}}$ where γ is the thermal dissipation rate. Full article

We study the apparent duality between large and small ${\eta }_H$ for the constant-roll inflation with the second slow-roll parameter ${\eta }_H$ being a constant. In the previous studies, only the constant-roll inflationary models with small ${\eta }_H$ are found to be consistent with the observations. The apparent duality suggests that the constant-roll inflationary models with large ${\eta }_H$ may be also consistent with the observations. We find that the duality between the constant-roll inflation with large and small ${\eta }_H$ does not exist, because both the background and scalar perturbation evolutions are very different. By fitting the constant-roll inflationary models to the observations, we get $-0.016\le {\eta }_H\le -0.0078$ at the 95% C.L if we take $N=60$ for the models with increasing ${ϵ}_H$ , in which inflation ends when ${ϵ}_H=1$ . For the models with decreasing ${ϵ}_H$ , we obtain $3.0135\le {\eta }_H\le 3.021$ at the 68% C.L. and $3.0115\le {\eta }_H\le 3.024$ at the 95% C.L. Full article

The swampland criteria are generically in tension with single-field slow-roll inflation because the first swampland criterion requires small tensor-to-scalar ratio while the second swampland criterion requires either large tensor-to-scalar ratio or large scalar spectral tilt. The challenge to single-field slow-roll inflation imposed by the swampland criteria can be avoided by modifying the relationship between the tensor-to-scalar ratio and the slow-roll parameter. We show that the Gauss–Bonnet inflation with the coupling function inversely proportional to the potential overcomes the challenge by adding a constant factor in the relationship between the tensor-to-scalar ratio and the slow-roll parameter. For the Gauss–Bonnet inflation, while the swampland criteria are satisfied, the slow-roll conditions are also fulfilled, so the scalar spectral tilt and the tensor-to-scalar ratio are consistent with the observations. We use the potentials for chaotic inflation and the E-model as examples to show that the models pass all the constraints. The Gauss–Bonnet coupling seems a way out of the swampland issue for single-field inflationary models. Full article

A new gravity model with the function F(R) = (1/β) arctan (βR – β²R²) instead of the Ricci scalar in the Einstein–Hilbert action, describing inflation of the Universe, is suggested and analyzed. We obtain constant curvature solutions of the model in the Jordan frame. Performing the conformal transformation of the metric, the potential and the mass of a scalar degree of freedom in the Einstein frame are found. The slow-roll and cosmological parameters of the model are evaluated. It was demonstrated that the index of the scalar spectrum power law, n_s, is in agreement with the PLANCK data. Full article