Is the squeezing of relic gravitational waves produced by inflation detectable?

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 61, Issue 2, 2000, Pages

  Papa, Maria Alessandra ^c  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

^b Department of Population Medicine and Diagnostic Sciences   (United States)

^c INFN LABORATORI NAZIONALI DI FRASCATI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044377786     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.61.024024     Document Type: Article

References (35)

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10. A good general review of the LISA project is the Proceedings of the Second International LISA Symposium, Pasadena, 1998, edited by W. Folkner, AIP Conf. Proc. No. 456 (American Institute of Physics, Woodbury, NY, 1998).
11. L.P. Grishchuk, “The detectability of relic (squeezed) gravitational waves by laser interferometers,” gr-qc/9810055.
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13. L. P. Grishchuk, in “Workshop on squeezed states and uncertainty relations,” NASA Conf. Publ. 3135, 1992, p. 329
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15. D. Polarski and A.A. Starobinsky, Class. Quantum Grav. 13, 377 (1996). A similar discussion but in the context of scalar rather than tensor perturbations is given in Ref. 15.
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17. Reference 11 refers to the signal-to-noise ratio (SNR) growing as (or faster than) than the fourth root of the observation time, because there the signal is an amplitude. This is equivalent to our discussion, where the signal (Formula presented) or some filtered version of it] is an amplitude squared (a power) proportional to (Formula presented) growing as (or faster than) the square root of the observation time. See for example Eq. (3.33) of Ref. 5 or Eq. (3.75) of Ref. 6.
18. A. Albrecht, “Coherence and Sakharov Oscillations in the Microwave Sky,” astro-ph/9612015.
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20. J. Lesgourgues, D. Polarski, S. Prunet, and A.A. Starobinsky, “Detectability of the primordial origin of the gravitational wave background in the Universe,” gr-qc/9906098, 1999.
21. An example that illustrates the necessity of such an analysis is the hoped-for detection of coalescing compact binaries with LIGO, where the overall signal is detectable, but where nevertheless the signal in each individual time bin of the data is small compared to the noise in that bin.
22. Michael S. Turner, Phys. Rev. D 55, 435 (1997).
23. B. Allen and S. Koranda, Phys. Rev. D 50, 3713 (1994).
24. The reason for this is as follows. The discussion of the previous paragraph applies only to modes of fields for which geometric optics is valid. Modes which “leave the horizon” during inflation violate this assumption, and are parametrically amplified. Now those modes which are inside the horizon today and which were subject to parametric amplification (i.e., at some stage left the horizon) had physical wavelengths (Formula presented) at the beginning of inflation in the range (Formula presented)where (Formula presented) is the Hubble constant during inflation, N is the number of efoldings during inflation, (Formula presented) is the redshift of matter-radiation equality, and (Formula presented) is the redshift of the end of inflation. From the parameter values in Sec. III B, we see that these wavelengths are so tiny that it is natural to assume that the corresponding modes all started in their vacuum states at the beginning of inflation. This is the assumption that is usually made.
25. L.P. Grishchuk, Zh. Eksp. Teor. Fiz. 67, 825 (1974) [Sov. Phys. JETP 40, 409 (1975)].
26. See the discussion and references in B. Allen, Phys. Rev. D 37, 2078 (1988).
27. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).
28. L. Parker, Phys. Rev. 183, 1057 (1969), particularly the discussion following Eq. (50). This early paper incorrectly states that there is no particle production for a massless field — this was corrected in later work
29. L. Parker, Phys. Rev. D 12, 1519 (1975), particularly the discussion between Eqs. (34) and (40).
30. E. Flanagan, Phys. Rev. D 48, 2389 (1993).
31. Strictly speaking (Formula presented) is a quantum mechanical operator; see Sec. III. However, the commutator (Formula presented) is smaller than the quantity (A5) by a factor (Formula presented) which is negligible in the limit of large squeezing (Formula presented) (ensured by the large number of efolds during inflation). Thus it is a good approximation to treat (Formula presented) as classical random processes.
32. Note that the corresponding equation in footnote 21 of Ref. 29 has a typo; the (Formula presented) should be corrected to (Formula presented) Also the right-hand side of Eq. (2.8) of Ref. 29 should be divided by (Formula presented)
33. L.P. Grishchuk and M. Solokhin, Phys. Rev. D 43, 2566 (1991). See in particular the equation before Eq. (18).
34. Observations that start at (Formula presented) (which is of course unrealistic) can easily distinguish between the stationary and squeezed cases, since the initial time derivative (Formula presented) is constrained to vanish in the squeezed case, by Eqs. (2.11) and (2.13).
35. This is most easily derived by using (Formula presented)Note also that the frequency f is a physical frequency and not a coordinate frequency.