# Cosmology in Scalar-Tensor Gravity by Valerio Faraoni

By Valerio Faraoni

**Cosmology in Scalar-Tensor Gravity** covers all points of cosmology in scalar-tensor theories of gravity. substantial growth has been made during this interesting zone of physics and this booklet is the 1st to supply a severe evaluate of the study. one of the themes handled are:

-Scalar-tensor gravity and its restrict to common relativity,

-Effective energy-momentum tensors and conformal frames,

-Gravitational waves in scalar-tensor cosmology,

-Specific scalar-tensor theories,

-Exact cosmological options and cosmological perturbations,

-Scalar-tensor eventualities of the early universe and inflation,

-Scalar-tensor types of quintessence within the current universe and their far-reaching outcomes for the final word destiny of the cosmos.

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97) yields 4> dVd + 2V] . 103) By substituting into the last equation the values of H 2 and of D ¢ obtained, respectively, from eq. 106) ¢ These equations differ from the equations of BD cosmology by the terms in w = dw / drj>, and by the fact that now is a function of ¢ .. Only two of the equations and are independent. From the cosmological point of view, a time-dependent parameter ¢ ( is more attractive than the constant parameter of BD theory. In a FLRW universe, ¢ and ¢) only depend on the cosmic time This opens the door to the possibility that be of order unity in the early universe.

Other authors discard the Einstein frame as unphysical and only accept the Jordan frame as physical. Finally, a third class of authors regard the Jordan frame and the Einstein frame with fixed units as physically equivalent, which is incorrect. This issue is discussed in de tail in the next chapter: first we expose the mathematical technique of conformal transformations. l G o2 9ab ' ( 1. 1 4 1 ) 34 COSMOLOGY IN SCALAR- TENSOR GRAVITY where the conformal factor O(x) is a nowhere vanishing, regular5 func tion, is called a Weyl or conformal transformation.

Eq. J> 0. 180) By introducing an affine parameter along the fluid worldlines with tangent eq. 181) � "V- a yftWT Scalar-tensor gravity 41 d-(P m) + p-(m) Vcuc = d).. equivalent to _ _ _ and 0 (1. 182) ( 1 . 1 83) The geodesic equation is then modified according to [887, 221 , 223] ( 1 . 1 84) in the Einstein frame. There is a fifth force proportional to the gradient of ¢ that couples in the same way to any massive test particle. Because of this coupling, scalar-tensor theories in the Einstein frame are non metric theories.