The semiclassical gravitational path integral and random matrices (toward a microscopic picture of a dS2 universe)

We study the genus expansion on compact Riemann surfaces of the gravitational path integral $$ {\mathcal{Z}}_{\mathrm{grav}}^{(m)} $$ Z grav m in two spacetime dimensions with cosmological constant Λ > 0 coupled to one of the non-unitary minimal models ℳ2m − 1, 2. In the semiclassical limit, corresponding to large m, $$ {\mathcal{Z}}_{\mathrm{grav}}^{(m)} $$ Z grav m admits a Euclidean saddle for genus h ≥ 2. Upon fixing the area of the metric, the path integral admits a round two-sphere saddle for h = 0. We show that the OPE coefficients for the minimal weight operators of ℳ2m − 1, 2 grow exponentially in m at large m. Employing the sewing formula, we use these OPE coefficients to obtain the large m limit of the partition function of ℳ2m − 1, 2 for genus h ≥ 2. Combining these results we arrive at a semiclassical expression for $$ {\mathcal{Z}}_{\mathrm{grav}}^{(m)} $$ Z grav m . Conjecturally, $$ {\mathcal{Z}}_{\mathrm{grav}}^{(m)} $$ Z grav m admits a completion in terms of an integral over large random Hermitian matrices, known as a multicritical matrix integral. This matrix integral is built from an even polynomial potential of order 2m. We obtain explicit expressions for the large m genus expansion of multicritical matrix integrals in the double scaling limit. We compute invariant quantities involving contributions at different genera, both from a matrix as well as a gravity perspective, and establish a link between the two pictures. Inspired by the proposal of Gibbons and Hawking relating the de Sitter entropy to a gravitational path integral, our setup paves a possible path toward a microscopic picture of a two-dimensional de Sitter universe.

Investigation on an Nflation phase diagram with multifield polynomial potential

This study aims to investigate an Nflationary phase diagram with a multifield polynomial potential. The gradual vanishing of the inflationary phase during slow roll phase of the Nflation model has been demonstrated for a large number of fields in the case when there are voluminous [Formula: see text] phase transitions occurring in it. A phase diagram for Nflation model illustrates its phase transitions for a multifield potential [Formula: see text]. We use Marčenko–Pastur law to find likely distribution of different mass-scales of the fields. Further, the study for the conditions of entropy is carried out in the form of a bound that conforms to the number of e-folds [Formula: see text] and the number of fields [Formula: see text]. These drive Nflationary phase and are mostly responsible for the phenomena taking place in it. We investigate in addition, that all the de Sitter entropy in the neighborhood of the critical point is concentrated around it and is largely condensed in the number of fields [Formula: see text] for the selected potential.

Double peaks of gravitational wave spectrum induced from inflection point inflation

We investigate the possibility of inducing the gravitational waves (GWs) with double peak energy spectrum from primordial scalar perturbations in inflationary models with three inflection points. Here the inflection points can be generated from a polynomial potential or generated from a Higgs-like $$\phi ^4$$ ϕ 4 potential with the running of quartic coupling. In such models, the inflection point at large scales predicts the scalar spectral index and tensor-to-scalar ratio to be consistent with current CMB constraints, and the other two inflection points generate two large peaks in the scalar power spectrum at small scales, which can induce GWs with a double peak energy spectrum. We find that for some choices of the parameters the double peak spectrum can be detected by future GW detectors, and one of the peaks around $$f\simeq 10^{-9}{-}10^{-8}$$ f ≃ 10 - 9 - 10 - 8 Hz can also explain the recent NANOGrav signal. Moreover, the peaks of the power spectrum allow for the generation of primordial black holes, which accounts for a significant fraction of dark matter.

Symmetry factors of Feynman diagrams and the homological perturbation lemma

We discuss the symmetry factors of Feynman diagrams of scalar field theories with polynomial potential. After giving a concise general formula for them, we present an elementary and direct proof that when computing scattering amplitudes using the homological perturbation lemma, each contributing Feynman diagram is indeed included with the correct symmetry factor.

Relocalization switch in a triple quantum dot molecule in 2D

A symmetric chain of three quantum dots (i.e., one of the simplest quantum dot molecules) is constructed using a three-parametric non-separable version of an asymptotically separable sextic polynomial potential [Formula: see text]. The probability density [Formula: see text] (admitting either the central or off-central dominance) is assumed measured. A dynamical regime is found with an enhanced sensitivity of the central—off-central transition to the parameters. Quantitatively, the possibility of control of such a switch alias “relocalization catastrophe” is illustrated non-numerically.

GLOBAL SUBELLIPTIC ESTIMATES FOR KRAMERS–FOKKER–PLANCK OPERATORS WITH SOME CLASS OF POLYNOMIALS

In this article, we study some Kramers–Fokker–Planck operators with a polynomial potential $V(q)$ of degree greater than two having quadratic limiting behaviour. This work provides an accurate global subelliptic estimate for Kramers–Fokker–Planck operators under some conditions imposed on the potential.