Abstract. We study the structure of neutron stars in perturbative f (R) gravity models with realistic equations of state. We obtain mass-radius relations in a gravity model of the form f (R) = R+αR 2 . We find that deviations from the results of general relativity, comparable to the variations due to using different equations of state (EoS'), are induced for |α| ∼ 10 9 cm 2 . Some of the soft EoS' that are excluded within the framework of general relativity can be reconciled with the 2 solar mass neutron star recently observed for certain values of α within this range. For some of the EoS' we find that a new solution branch, which allows highly massive neutron stars, exists for values of α greater than a few 10 9 cm 2 . We find constraints on α for a variety of EoS' using the recent observational constraints on the mass-radius relation. These are all 5 orders of magnitude smaller than the recent constraint obtained via Gravity Probe B for this gravity model. The associated length scale √ α ∼ 10 5 cm is only an order of magnitude smaller than the typical radius of a neutron star, the probe used in this test. This implies that real deviations from general relativity can be even smaller.

We consider a toy cosmological model with a gas of wrapped Dp-branes in 10-dimensional dilaton gravity compactified on a p-dimensional Ricci flat internal manifold. A consistent generalization of the low energy effective field equations in the presence of a conserved brane source coupled to dilaton is obtained. It is then shown that the compact dimensions are dynamically stabilized in string frame as a result of a balance between negative winding and positive momentum pressures. Curiously, when p = 6, i.e. when the observed space is three dimensional, the dilaton becomes a constant and stabilization in Einstein frame is also realized.One of the main problems of string cosmology is to determine why the extra compact dimensions evolve differently from the observed three dimensions and remained comparatively very small. In [1], an intuitive mechanism was proposed to accommodate this difference where strings winding extra dimensions fall out of thermal equilibrium and stop the cosmological expansion. In [2][3][4][5], the arguments of [1] are quantified by demonstrating stabilization in Einstein and dilaton gravities using the energy momentum tensor for string winding and momentum modes on the torus (see also [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] for recent work on brane gas cosmology).As pointed out in [6], strings may not be able to stabilize extra dimensions when topology is different than a torus. Considering, for example, a spherical internal space, there exists no stable winding strings in the spectrum. One would then wonder if the higher dimensional branes can play a role in these compactifications. In [6], it is shown that a gas of p-branes wrapping over a pdimensional compact, Ricci flat, internal manifold can stabilize the volume modulus. As for strings, it turns out that there is a balance between the winding and the vibrational momentum modes. The results of [6] are obtained in Einstein gravity and the purpose of this letter is to generalize the framework to dilaton gravity. Here, it is natural to consider a toy model with a gas of winding Dbranes. Since dilaton couples to D-brane world-volume, it should be activated in this scenario.Our first aim is to generalize the equations of motion in the presence of a conserved source coupled to dilaton. In string frame, the low energy effective action (we set H µνρ = 0) is given bywhere we add a term to include the effects of matter governed by the Lagrangian L m . From this action, the field equations can be found aswhere T µν is the matter energy momentum tensorand the extra contribution F in (3) arises from the coupling of dilaton to L m . The conservation formula ∇ µ T µν = 0 plays the role of matter field equations. To determine the unknown function F we note the well known fact that (3) can be viewed as a consequence of (2) and the contracted Bianchi identity. Taking the divergence of (2) with ∇ µ , one finds:Although in general F cannot be uniquely fixed by this constraint, in a cosmological context one can assume thatwhere t is the t...

We examine spherical p-branes in AdS m ϫS n that wrap an S p in either AdS m (pϭmϪ2) or S n (pϭn Ϫ2). We first construct a two-spin giant solution expanding in S n and has spins both in AdS m and S n . For (m,n)ϭ͕(5,5),(4,7),(7,4)͖, it is 1/2 supersymmetric, and it reduces to the single-spin giant graviton when the AdS spin vanishes. We study some of its basic properties such as instantons, noncommutativity, zero modes, and the perturbative spectrum. All vibration modes have real and positive frequencies determined uniquely by the spacetime curvature, and evenly spaced. We next consider the ͑0ϩ1͒-dimensional sigma models obtained by keeping generally time-dependent transverse coordinates, describing a warped product of a breathing mode and a point particle on S n or AdS m ϫS 1 . The Bogomol'nyi-Prasad-Sommerfield bounds show that the only spherical supersymmetric solutions are the single and the two-spin giants. Moreover, we integrate the sigma model and separate the canonical variables. We quantize exactly the point-particle part of the motion, which in local coordinates gives Pöschl-Teller type potentials, and calculate its contribution to the anomalous dimension.

We study the structure of neutron stars in scalar-tensor theories for the nonminimal coupling of the form (1 + κξφ 2 )R. We solve the hydrostatic equilibrium equations for two different types of scalar field potentials and three different equations of state representative of different degrees of stiffness. We obtain the mass-radius relations of the configurations and determine the allowed ranges for the term ξφ 2 at the center of the star and spatial infinity based on the measured maximum value of the mass for neutron stars and the recent constraints on the radius coming from gravitational wave observations. Thus we manage to limit the deviation of the model from general relativity. We examine the possible constraints on the parameters of the model and compare the obtained restrictions with the ones inferred from other cosmological probes that give the allowed ranges for the coupling constant only. In the case of the Higgs-like potential, we also find that the central value for the scalar field cannot be chosen arbitrarily but it depends on the vacuum expectation value of the field. Finally, we discuss the effect of the scalar field potential on the mass and the radius of the star by comparing the results obtained for the cases considered here.

We consider a toy cosmological model in string theory involving the winding and momentum modes of (m, n) strings, i.e. bound states of m fundamental and n D-strings. The model is invariant under S-duality provided that m and n are interchanged. The dilaton is naturally stabilized due to S-duality invariance, which offers a new mechanism of moduli fixing in string gas cosmology. Using a tachyon field rolling down to its ground state, we also point out a possible way of realizing a cosmological phase with decreasing Hubble radius and constant dilaton.