Using pulsar timing arrays and the quantum normalization condition to constrain relic gravitational waves

In the non-standard model of relic gravitational waves (RGWs) generated in the early universe, the theoretical spectrum is mainly described by an amplitude r and a spectral index β, the latter usually being determined by the slope of the inflaton potential. Pulsar timing arrays (PTAs) data have imposed constraints on the amplitude of strain spectrum for a power-law form as a phenomenological model. Applying these constraints to a generic, theoretical spectrum with r and β as independent parameters, we convert the PTAs constraint into an upper bound on the index β, which turns out to be less stringent than those upper bounds from the Big Bang nucleosynthesis, cosmic microwave background and LIGO/VIRGO, respectively. Moreover, it is found that PTAs constrain the non-standard RGWs more stringently than the standard RGWs. If the condition of the quantum normalization is imposed upon a theoretical spectrum of RGWs, r and β become related. With this condition, a minimum requirement of the horizon size during inflation is greater than the Planck length that results in an upper bound on β, which is comparable in magnitude to that by PTAs. When both PTAs and the quantum normalization are applied to a theoretical spectrum of RGWs, constraints can be obtained for other cosmic processes of the early universe, such as the reheating, a process less understood observationally so far. The resulting constraint is consistent with the slow-roll, massive scalar inflation model. The future square kilometer array will be able to constrain RGWs further and might even detect RGWs, rendering an important probe to the very early universe.

Note:

Accepted for publication in Class. Quant. Grav

inflation: model
horizon: size
pulsar
cosmic background radiation
gravitational radiation: power spectrum
reheating
scale: Planck
VIRGO
LIGO
inflaton: potential

References(113)

Figures(8)

[1]

Amplification of gravitational waves in an istropic universe

L.P. Grishchuk
(
- Sternberg Astron. Inst.
)

- Sov.Phys.JETP 40 (1975) 409-415,
- Zh.Eksp.Teor.Fiz. 67 (1974) 825-838

[1]

The Implications of the microwave background anisotropies for laser interferometer tested gravitational waves

L.P. Grishchuk
(
- Cardiff U. and
- Moscow State U.
)

- Class.Quant.Grav. 14 (1997) 1445-1454
•
e-Print:
- gr-qc/9609062
•
DOI:
- 10.1088/0264-9381/14/6/009

[2]

Relic gravitational waves and their detection

L.P. Grishchuk
(
- Cardiff U. and
- Sternberg Astron. Inst.
)

- Lect.Notes Phys. 562 (2001) 167-194,
•
e-Print:
- gr-qc/0002035
•
DOI:
- 10.1007/3-540-40988-2_9

[3]

Relic gravitational waves and cosmology

L.P. Grishchuk
(
- Cardiff U.
)

- Phys.Usp. 48 (2005) 1235-1247
•
e-Print:
- gr-qc/0504018
•
DOI:
- 10.1070/PU2005v048n12ABEH005795

[4]

Discovering Relic Gravitational Waves in Cosmic Microwave Background Radiation

L.P. Grishchuk
(
- Cardiff U. and
- Sternberg Astron. Inst.
)

[5]

Spectrum of relict gravitational radiation and the early state of the universe

Alexei A. Starobinsky
(
- Landau Inst.
)

- JETP Lett. 30 (1979) 682-685,
- Pisma Zh.Eksp.Teor.Fiz. 30 (1979) 719-723,

[5]

Cosmic Background Anisotropy Induced by Isotropic Flat-Spectrum Gravitational-Wave Perturbations

A.A. Starobinsky

- Sov.Astron.Lett. 11 (1985) 133,
- Pisma Astron.Zh. 11 (1985) 323

[5]

Graviton Creation in the Inflationary Universe and the Grand Unification Scale

V.A. Rubakov
(
- Moscow, INR
)
,
M.V. Sazhin
(
- Sternberg Astron. Inst.
)
,
A.V. Veryaskin
(
- Sternberg Astron. Inst.
)

- Phys.Lett.B 115 (1982) 189-192
•
DOI:
- 10.1016/0370-2693(82)90641-4

[5]

The Effect of Primordially Produced Gravitons upon the Anisotropy of the Cosmological Microwave Background Radiation

R. Fabbri
(
- Florence U.
)
,
M.d. Pollock
(
- Padua U.
)

- Phys.Lett.B 125 (1983) 445-448
•
DOI:
- 10.1016/0370-2693(83)91322-9

[5]

Constraints on Generalized Inflationary Cosmologies

L.F. Abbott
(
- Brandeis U.
)
,
Mark B. Wise
(
- Caltech
)

- Nucl.Phys.B 244 (1984) 541-548
•
DOI:
- 10.1016/0550-3213(84)90329-8

[5]

The Stochastic Gravity Wave Background in Inflationary Universe Models

Bruce Allen
(
- Tufts U.
)

- Phys.Rev.D 37 (1988) 2078
•
DOI:
- 10.1103/PhysRevD.37.2078

[5]

The Energy Density of Relic Gravity Waves From Inflation

Varun Sahni
(
- Canadian Inst. Theor. Astrophys.
)

- Phys.Rev.D 42 (1990) 453-463
•
DOI:
- 10.1103/PhysRevD.42.453

[5]

Reheating after quintessential inflation and gravitational waves

Hiroyuki Tashiro
(
- Kyoto U.
)
,
Takeshi Chiba
(
- Kyoto U.
)
,
Misao Sasaki
(
- Kyoto U., Yukawa Inst., Kyoto
)

- Class.Quant.Grav. 21 (2004) 1761-1772
•
e-Print:
- gr-qc/0307068
•
DOI:
- 10.1088/0264-9381/21/7/004

[5]

The stochastic gravitational - wave background and the inflation to radiation transition in the early universe

Alfredo B. Henriques
(
- Lisbon, CENTRA
)

- Class.Quant.Grav. 21 (2004) 3057,
- Class.Quant.Grav. 24 (2007) 6431-6434 (erratum)
•
e-Print:
- astro-ph/0309508
•
DOI:
- 10.1088/0264-9381/24/24/C01