Relating gravitational wave constraints from primordial nucleosynthesis, pulsar timing, laser interferometers, and the CMB: Implications for the early universe

Journal Article · Fri Aug 15 00:00:00 EDT 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.78.043531· OSTI ID:21250479

Boyle, Latham A ^[1]; Buonanno, Alessandra ^[2]

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1. Canadian Institute for Theoretical Astrophysics (CITA), University of Toronto, 60 St. George Street, Toronto, Ontario, M5S 3H8 (Canada)
2. Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742 (United States)

We derive a general equation relating the gravitational-wave observables r and {omega}{sub 0}{sup gw}(f); or the observables {omega}{sub 0}{sup gw}(f{sub 1}) and {omega}{sub 0}{sup gw}(f{sub 2}). Here, r is the so-called 'tensor-to-scalar ratio', which is constrained by cosmic-microwave-background experiments; and {omega}{sub 0}{sup gw}(f) is the energy spectrum of primordial gravitational waves, which is constrained, e.g., by pulsar-timing measurements, laser-interferometer experiments, and the standard big bang nucleosynthesis bound. Differentiating this equation yields a new expression for the tilt dln{omega}{sub 0}{sup gw}(f)/dlnf of the present-day gravitational-wave spectrum. The relationship between r and {omega}{sub 0}{sup gw}(f) depends sensitively on the uncertain physics of the early universe, and we show that this uncertainty may be encapsulated (in a model-independent way) by two quantities: w-circumflex(f) and n-circumflex{sub t}(f), where n-circumflex{sub t}(f) is a certain logarithmic average over n{sub t}(k) (the primordial tensor spectral index); and w-circumflex(f) is a certain logarithmic average over w-tilde(a) (the effective equation-of-state parameter in the early universe, after horizon re-entry). Here, the effective equation-of-state parameter w-tilde(a) is a combination of the ordinary equation-of-state parameter w(a) and the bulk viscosity {zeta}(a). Thus, by comparing observational constraints on r and {omega}{sub 0}{sup gw}(f), one obtains (remarkably tight) constraints in the {l_brace}w-circumflex(f),n-circumflex{sub t}(f){r_brace} plane. In particular, this is the best way to constrain (or detect) the presence of a stiff energy component (with w>1/3) in the early universe, prior to big bang nucleosynthesis. (The discovery of such a component would be no more surprising than the discovery of a tiny cosmological constant at late times{exclamation_point}) Finally, although most of our analysis does not assume inflation, we point out that if cosmic-microwave-background experiments detect a nonzero value for r, then we will immediately obtain (as a free by-product) a new upper bound w-circumflex < or approx. 0.55 on the logarithmically averaged effective equation-of-state parameter during the 'primordial dark age' between the end of inflation and the start of big bang nucleosynthesis.

• OSTI ID: 21250479
• Journal Information: Physical Review. D, Particles Fields, Vol. 78, Issue 4; Other Information: DOI: 10.1103/PhysRevD.78.043531; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCELERATION
COSMIC RADIATION
COSMOLOGICAL CONSTANT
COSMOLOGY
ENERGY SPECTRA
EQUATIONS OF STATE
GRAVITATIONAL WAVES
INTERFEROMETERS
INTERFEROMETRY
LASER RADIATION
NUCLEOSYNTHESIS
PULSARS
RADIOWAVE RADIATION
RELICT RADIATION
SIMULATION
UNIVERSE