Rosmarinic acid improves intestinal barrier integrity through PI3K/AKT/Nrf2-mediated regulation of tight junction protein expression.

Rosmarinic acid (RA), a polyphenolic compound, exhibits diverse pharmacological activities, including anti-inflammatory, antioxidant, and antitumor effects. Despite its therapeutic potentials, the mechanisms underlying its efficacy in ulcerative colitis (UC), a chronic inflammatory bowel disease characterized by intestinal epithelial barrier dysfunction, remain incompletely elucidated. This study investigates RA's protective effects in UC using complementary in vivo and in vitro models.

Extended δN Formalism: Nonspatially Flat Separate-Universe Approach.

The δN formalism is a powerful approach to compute nonlinearly the large-scale evolution of the comoving curvature perturbation ζ. It assumes a set of FLRW patches that evolve independently, but in doing so, all the gradient terms are discarded, which are not negligibly small in models beyond slow roll. In this Letter, we extend the formalism to capture these gradient corrections by encoding them in a homogeneous-spatial-curvature contribution assigned to each FLRW patch.

Logarithmic Duality of the Curvature Perturbation.

We study the comoving curvature perturbation R in the single-field inflation models whose potential can be approximated by a piecewise quadratic potential V(φ) by using the δN formalism. We find a general formula for R(δφ,δπ), consisting of a sum of logarithmic functions of the field perturbation δφ and the velocity perturbation δπ at the point of interest, as well as of δπ_{*} at the boundaries of each quadratic piece, which are functions of (δφ,δπ) through the equation of motion. Each logarithmic expression has an equivalent dual expression, due to the second-order nature of the equation of motion for φ.

Gravitational Waves Induced by Non-Gaussian Scalar Perturbations.

We study gravitational waves (GWs) induced by non-Gaussian curvature perturbations. We calculate the density parameter per logarithmic frequency interval, Ω_{GW}(k), given that the power spectrum of the curvature perturbation P_{R}(k) has a narrow peak at some small scale k_{*}, with a local-type non-Gaussianity, and constrain the nonlinear parameter f_{NL} with the future LISA sensitivity curve as well as with constraints from the abundance of the primordial black holes (PBHs). We find that the non-Gaussian contribution to Ω_{GW} increases as k^{3}, peaks at k/k_{*}=4/sqrt[3], and has a sharp cutoff at k=4k_{*}.