Nonminimally coupled scalar fields in homogeneous universes

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 61, Issue 8, 2000, Pages

  Alberghi, G L ^a   Casadio, R ^a   Gruppuso, A ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

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Indexed keywords

EID: 17044380549     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.61.084009     Document Type: Article

References (34)

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22. We remark that the full scalar field (Formula presented) couples to gravity for (Formula presented) Alternatively one might want to couple R only to quantum fluctuations by setting (Formula presented) and replacing the factor (Formula presented) which multiplies R with (Formula presented) but we shall not attempt at this in the present paper.
23. In this paper we shall refer to the case with (Formula presented) as to the conformally coupled scalar field, although, strictly speaking, such denomination also requires (Formula presented) 1.
24. One could try to define a new canonical variable (Formula presented) such that its conjugate momentum is (Formula presented) and diagonalizes the kinetic term in Eq. (2.16). However, we observe that the explicit form of (Formula presented) as determined by the condition (Formula presented) where F is an arbitrary function, would shift the Hamiltonian, (Formula presented) and necessarily mix the gravitational and matter degrees of freedom (for (Formula presented) to wit (Formula presented) The latter fact places serious questions on the definition of the semiclassical limit for gravity as described in the Introduction, since one cannot disentangle matter from gravity after such a canonical transformation has been performed.
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26. One could avoid most of such formal problems by assuming that the (semiclassical) variable a is eventually the only physical observable in the system. Since a determines the relative positions of freely falling (comoving) points in the Robertson-Walker manifold and space-time points in general relativity are defined only when a material reference frame is introduced 1121, this also requires the existence of some (semi)classical matter whose “weight” we shall identify in Eq. (3.50) with the quantity (Formula presented) given in Eq. (3.46).
27. More precisely, there is only one state (Formula presented) such that (Formula presented) and this gives the classical evolution with (Formula presented)
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