Introduction
The habitable zone is commonly defined in reference to a distance from a luminous source, such as a star (Kasting et al. Reference Kasting, Whitmire and Reynolds1993; Kasting Reference Kasting2010), whose heat maintains the surface of a rocky planet at a temperature of ~300 K, allowing liquid water to exist and the chemistry of ‘life as we know it’ to operate. In this brief paper, I point out that the cosmic microwave background (CMB) provided a uniform heating source at a temperature of T cmb=272.6 K×[(1+z)/100] (Fixsen Reference Fixsen2009) that could have made by itself rocky planets habitable at redshifts (1+z)=100–137 in the early Universe, merely 10–17 million years after the Big Bang.
In order for rocky planets to exist at these early times, massive stars with tens to hundreds of solar masses, whose lifetime is much shorter than the age of the Universe, had to form and enrich the primordial gas with heavy elements through winds and supernova explosions (Ober et al. Reference Ober, El Eid and Fricke1983; Heger & Woosley Reference Heger and Woosley2002). Indeed, numerical simulations predict that predominantly massive stars have formed in the first halos of dark matter to collapse (Bromm & Larson Reference Bromm and Larson2004; Loeb & Furlanetto Reference Loeb and Furlanetto2012). For massive stars that are dominated by radiation pressure and shine near their Eddington luminosity L E=1.3×10 erg s−1(M */100 M ⊙), the lifetime is independent of the stellar mass M * and set by the 0.7% nuclear efficiency for converting the rest mass to radiation, ~(0.007 M * c 2)/L E=3 Myr (El Eid et al. Reference El Eid, Fricke and Ober1983; Bromm et al. Reference Bromm, Kudritzki and Loeb2001; Marigo et al. Reference Marigo, Chiosi, Girardi and Kudritzki2003). We next examine how early such stars formed within the observable volume of our Universe.
First planets
In the standard cosmological model, structures form hierarchically – starting from small spatial scales, through the gravitational growth of primordial density perturbations (Loeb & Furlanetto Reference Loeb and Furlanetto2012). On any given spatial scale R, the probability distribution of fractional density fluctuations δ is assumed to have a Gaussian form, P(δ)dδ=(2πσ2)−1/2 exp{−δ 2 /2σ2}dδ, with a root-mean-square amplitude σ(R) that is initially much smaller than unity. The initial σ(R) is tightly constrained on large scales, R≳1 Mpc, through observations of the CMB anisotropies and galaxy surveys (Ade et al. Reference Ade2013a; Anderson et al. Reference Anderson2014), and is extrapolated theoretically to smaller scales. Throughout the paper, we normalize spatial scales to their so-called ‘comoving’ values in the present-day Universe. The assumed Gaussian shape of P(δ) has so far been tested only on scales R≳1 Mpc for δ≲3σ (Shandera et al. Reference Shandera, Mantz, Rapetti and Allen2013), but was not verified in the far tail of the distribution or on small scales that are first to collapse in the early Universe.
As the density in a given region rises above the background level, the matter in it detaches from the Hubble expansion and eventually collapses owing to its self-gravity to make a gravitationally bound (virialized) object like a galaxy. The abundance of regions that collapse and reach virial equilibrium at any given time depends sensitively on both P(δ) and σ(R). Each collapsing region includes a mix of dark matter and ordinary matter (often labelled as ‘baryonic’). If the baryonic gas is able to cool below the virial temperature inside the dark matter halo, then it could fragment into dense clumps and make stars.
At redshifts z≳140 Compton cooling on the CMB is effective on a timescale comparable to the age of the Universe, given the residual fraction of free electrons left over from cosmological recombination (see section 2.2 in Loeb & Furlanetto (Reference Loeb and Furlanetto2012) and Pritchard & Loeb (Reference Pritchard and Loeb2012)). The thermal coupling to the CMB tends to bring the gas temperature to T cmb, which at z~140 is similar to the temperature floor associated with molecular hydrogen cooling (Haiman et al. Reference Haiman, Thoul and Loeb1996; Tegmark et al. Reference Tegmark, Silk, Rees, Blanchard, Abel and Pella1997; Hirata & Padmanabhan Reference Hirata and Padmanabhan2006). In order for virialized gas in a dark matter halo to cool, condense and fragment into stars, the halo virial temperature T vir has to exceed T min≈300 K, corresponding to T cmb at (1+z)~110. This implies a halo mass in excess of M min=104 M ⊙, corresponding to a baryonic mass M b,min=1.5×103 M ⊙, a circular virial velocity V c,min=2.6 km s−1 and a virial radius r vir,min=6.3 pc (see section 3.3 in Loeb & Furlanetto Reference Loeb and Furlanetto2012). This value of M min is close to the minimum halo mass to assemble baryons at that redshift (see section 3.2.1 in Loeb & Furlanetto (Reference Loeb and Furlanetto2012) and Fig. 2 of Tseliakhovich et al. (Reference Tseliakhovich, Barkana and Hirata2011)).
The corresponding number of star-forming halos on our past light cone is given by (Naoz et al. Reference Naoz, Noter and Barkana2006),
$$N = \int_{(1 + z) = 100}^{(1 + z) = 137} {n(M \gt M_{\min}, z')} \displaystyle{{{\rm d}V} \over {{\rm d}z'}}{\rm d}z',$$
where n(M>M
min) is the comoving number density of halos with a mass M>M
min (Sheth & Tormen Reference Sheth and Tormen1999), and dV=4πr
2dr is the comoving volume element with dr=cdt/a(t). Here, a(t)=(1+z)−1 is the cosmological scale factor at time t, and
$r(z) = c\int_0^z {{\rm d}z'/H(z')} $
is the comoving distance. The Hubble parameter for a flat Universe is
$H(z) \equiv (\dot a/a) = H_0 \sqrt {\Omega _m (1 + z)^3 + \Omega _r (1 + z)^4 + \Omega _\Lambda } $
, with Ωm, Ωr and ΩΛ being the present-day density parameters of matter, radiation and vacuum, respectively. The total number of halos that existed at (1+z)~100 within our entire Hubble volume (not restricted to the light cone), N
tot
≡n(M>M
min, z=99)×(4π/3)(3c/H
0)3, is larger than N by a factor of ~103.
For the standard cosmological parameters (Ade et al. Reference Ade2013a), we find that the first star-forming halos on our past light cone reached its maximum turnaround radiusFootnote 1 (with a density contrast of 5.6) at z~112 and collapsed (with an average density contrast of 178) at z~71. Within the entire Hubble volume, a turnaround at z~122 resulted in the first collapse at z~77. This result includes the delay by Δz~5.3 expected from the streaming motion of baryons relative to the dark matter (Fialkov et al. Reference Fialkov, Barkana, Tseliakhovich and Hirata2012).
The above calculation implies that rocky planets could have formed within our Hubble volume by (1+z)~78 but not by (1+z)~110 if the initial density perturbations were perfectly Gaussian. However, the host halos of the first planets are extremely rare, representing just ~2×10−17 of the cosmic matter inventory. Since they lie ~8.5 standard deviations (σ) away on the exponential tail of the Gaussian probability distribution of the initial density perturbations, P(δ), their abundance could have been significantly enhanced by primordial non-Gaussianity (LoVerde & Smith Reference LoVerde and Smith2011; Maio et al. Reference Maio, Salvaterra, Moscardini and Ciardi2012; Musso & Sheth Reference Musso and Sheth2013) if the decline of P(δ) at high values of δ/σ is shallower than exponential. The needed level of deviation from Gaussianity is not ruled out by existing datasets (Ade et al. Reference Ade2013b). Non-Gaussianity below the current limits is expected in generic models of cosmic inflation (Maldacena Reference Maldacena2003) that are commonly used to explain the initial density perturbations in the Universe.
Discussion
In this brief paper, I highlighted a new regime of habitability made possible for ~6.6 Myr by the uniform CMB radiation at redshifts (1+z)=100–137, just when the first generation of star-forming halos (with a virial mass ≳104 M ⊙) turned around in the standard cosmological model with Gaussian initial conditions. Deviations from Gaussianity in the far (8.5σ) tail of the probability distribution of the initial density perturbations could have led already at these redshifts to the birth of massive stars, whose heavy elements triggered the formation of rocky planets with liquid water on their surface.Footnote 2
Thermal gradients are needed for life. These can be supplied by geological variations on the surface of rocky planets. Examples of sources of free energy are geothermal energy powered by the planet's gravitational binding energy at formation and radioactive energy from unstable elements produced by the earliest supernova. These internal heat sources (in addition to possible heating by a nearby star) may have kept planets warm even without the CMB, extending the habitable epoch from z~100 to later times. The lower CMB temperature at late times may have allowed ice to form on objects that delivered water to a planet's surface, and helped to maintain the cold trap of water in the planet's stratosphere. Planets could have kept a blanket of molecular hydrogen that maintained their warmth (Stevenson Reference Stevenson1999; Pierrehumbert & Gaidos Reference Pierrehumbert and Gaidos2011), allowing life to persist on internally warmed planets at late cosmic times. If life persisted at z≲100, it could have been transported to newly formed objects through panspermia (McNichol & Gordon Reference McNichol, Gordon and Seckbach2012). Under the assumption that interstellar panspermia is plausible, the redshift of z~100 can be regarded as the earliest cosmic epoch after which life was possible in our Universe.
The feasibility of life in the early Universe can be tested by searching for planets with atmospheric bio-signatures around low-metallicity stars in the Milky Way galaxy or its dwarf galaxy satellites. Such stars represent the closest analogues to the first generation of stars at early cosmic times.
The possibility that the chemistry of life could have started in our Universe only 10–17 Myr after the Big Bang is not in agreement with the anthropic explanationFootnote 3 for the value of the cosmological constant (Weinberg Reference Weinberg1987), especially if the characteristic amplitude of the initial density perturbations or the level of non-Gaussianity is allowed to vary in different regions of the multiverseFootnote 4 (Garriga & Vilenkin Reference Garriga and Vilenkin2006; Tegmark et al. Reference Tegmark, Aguirre, Rees and Wilczek2006). In principle, the habitable cosmological epoch considered here allows for life to emerge in a Universe with a cosmological constant that is (1+z)3~106 times bigger than observed (Loeb Reference Loeb2006). If observers can eventually emerge from primitive forms of life at an arbitrarily later time in such a Universe, then their existence would be in conflict with the anthropic reasoning for the low value of the cosmological constant in our Universe. Even when placed on a logarithmic scale, the corresponding discrepancy in the vacuum energy density is substantial, spanning ~5% of the ~120 orders of magnitude available up to the Planck density. The volume associated with inflating regions of larger vacuum density is exponentially greater than our region, making residence in them far more likely.
Acknowledgements
I thank F. Dyson, J. Maldacena, D. Maoz and E. Turner for useful comments on the manuscript. This work was supported in part by NSF grant AST-1312034.
