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The convergence of the cosmological tests from redundant constraints on the global cosmological parameters offers a good case for the LambdaCDM Friedmann-Lemaître cosmology as a useful approximation to the real world. This is a necessary condition that this compilation of the energy inventory is a meaningful exercise.

We adopt the working assumption that the galaxies are useful tracers of mass, in the sense that inventory entries derived under this assumption are good approximations to reality. This assumption has been widely questioned. However, the recent evidence from weak lensing (eqs. [3] to [7]), with the older evidence from the galaxy relative velocity dispersion at separations ~ 100 kpc to 1 Mpc, and the consistent picture for the virialized parts of field galaxies (eq. [10]), offer what seems to be a reliable case for the use of galaxies as mass tracers. The approach certainly is not exact, and working out more accurate measures of the mass distribution on the scale of galaxies remains an important and fascinating challenge.

Our other conventions for the cosmology are less controversial but may have to be adjusted. For simplicity, we have adopted a fixed distance scale (eq. [1]). We have not presented the scaling of inventory entries with the distance scale, which can be somewhat complicated; this issue is best revisited when the uncertainty in the distance scale is better understood. Our adopted value and formal uncertainty for the matter density parameter, Omegam (eq. [8]), is in the generally accepted range, but there is reason to suspect that it is somewhat overestimated (Section 2.1). Again, this is a issue to revisit when the constraints have improved. Our value for the baryon mass density agrees with what is derived from the CMBR anisotropy and the measurements of the primeval deuterium abundance, but it is larger than what is indicated by recent estimates of the primeval helium abundance. We have suggested in Section 2.2.2 that the problem may be with the technical difficulties of the helium measurements, but we will be following the advances in this subject with interest. It would not be surprising to see the discovery of richer physics in the dark sector, and with it an increase in the variety of entries in category 1, and possibly also some adjustment of other parts of the inventory that depend on the dark sector physics. One should also bear in mind that the alternative pictures of structure formation that were under discussion a decade ago, such as cosmic strings, could be operating as subdominant perturbations to the LambdaCDM model. Further progress in testing the model for structure formation will inform our ideas on whether the entries that depend on the theory of structure formation are likely to require adjustment. Each of these issues may be pointing to revisions to the inventory outside our stated errors. On the other hand, the successful network of tests of the cosmology and the model for structure formation leads us to expect that the general framework presented in Table 1 is not likely to change.

We have argued that 6 ± 1% of the baryons are in stars and stellar remnants (eqs. [16] and [27] with h = 0.7). This small fraction is analyzed in considerable detail in the inventory, in entries that are supported by a network of tests. The estimate in Section 2.7.1 of the mass density in stars uses the optical luminosity density and the stellar-mass-to-light ratio. The luminosity density is checked by measurements of the optical to near infrared intergalactic radiation energy density, and by the measured galaxy counts (Section 2.7.1). The comparison is not tight, but it shows that the radiation energy density likely is known to ± 0.3 dex. The conversion from the luminosity density to the stellar mass density depends on the model for the stellar initial mass function. The model we use is checked by the reasonable agreement with the ratio of the white dwarf to subsolar main sequence star densities at the low mass end, and with the global Type II supernova rate at the high mass end (2.3.1, 2.3.2). The model for the star formation history is based on the time history of the Halpha luminosity density, which is broadly consistent with other measures of the evolution of the star formation rate density. The model is checked by consistency with the accumulated mass in stars (after correction for mass loss; eq. [34]). Yet another check involves the accumulated mass density in heavy elements. The release of nuclear binding energy in the heavy elements, corrected for the loss of radiation energy by the cosmological redshift (eq. [35]), is in satisfactory agreement with the present radiation energy density at near optical and far infrared wavelengths (Section 2.7.3). This test would fail if there were a substantial amount of radiation energy at wavelengths 1µ < lambda < 100µ; improved measurements will be of considerable interest. This test also depends on the stellar production of helium, which is discussed in Section 2.2.2, in connection with the constraint on the baryon mass density from the primeval helium abundance, and in Section 2.8.1, from an analysis of the products of stellar evolution. The results seem reasonably consistent. The network of checks is complicated, but that is what lends credence to the results.

It is well to pause to consider Arp's (1965) cautionary remark, that there may be extragalactic objects with sizes too small to be readily distinguished from stars - an example is the quasi-stellar objects Arp mentions in a note added in proof - or with surface brightnesses too low to be readily seen against the foreground - an example is the intracluster light in the Virgo cluster (Arp & Bertola 1971). The quasar remnants could have contained a significant baryon mass, if the mass conversion efficiency epsilonn had been close to unity (eq. [73]), but we now know that that is difficult to reconcile with the integrated quasar energy emission (eq. [83]). There are low surface brightness objects (e.g McGaugh, Schombert, & Bothun 1995), but the surface brightness of the extragalactic sky shows that they cannot largely affect our estimate of the mean luminosity density (Section 2.7.1). Substellar objects might be counted as part of Arp's cautionary remark, but they are detectable in nearby galaxies by weak gravitational lensing (or MACHOs, as discussed by Alcock et al. 2001 and references therein). That is, a half century ago it was not clear that it is feasible to establish a fair observational census of the stars. Now it appears that the observational conditions allow it: the closure of our inventory suggests that missing or unknown components cannot be energetically very significant.

The network of tests of the baryon budget could be improved by using computations that exist or could be readily developed within existing computations, but that we could not readily assemble. In particular, the theoretical analyses of stellar remnants and the other products of stellar evolution (Sections 2.3.1 and 2.8), with special attention to the white dwarfs that store so much of the heavy elements, clearly will have to be done better as the observations improve.

The baryon number density - excluding baryons that may have been sequestered prior to light element production - seems to be reliably constrained, but the states of most of the baryons are not yet observationally well documented. The picture that galaxies trace mass leads us ot expect that about half the dark matter is gathered near and within the virialized parts of the galaxies (eq. [13]). Entries 3.1 and 3.2 in Table 1 are based on the assumption that the baryons are similarly placed, in the diffuse states observed as hot plasma in clusters of galaxies and in warm and hot plasma in and around groups of galaxies (eq. [56]). This has not yet been convincingly observationally demonstrated. We have not made much use of the predicted states of the baryons from numerical simulations, because we do not know how to judge the reliability of the predictions on relatively small scales. As the computations and their observational checks improve this will become clearer, and the results may be expected to improve this part of the inventory.

The advances in observations of the massive compact objects in the centers of galaxies allow an improved test of the idea that these objects are the black hole remnants of quasars and AGNs that are powered by gravitational accretion. The picture is consistent with the observations if the quasar mass conversion efficiency is epsilonn gtapprox 0.02, a reasonable-looking number. A tighter constraint on epsilonn awaits an improved quasar luminosity function at fainter magnitudes and at higher redshifts (Section 2.5.3).

The efficiency of conversion of mass into electromagnetic radiation in the formation of stellar mass black holes is constrained to be less than a few percent by the observed energy density in electromagnetic radiation and neutrinos. The interpretation of this constraint awaits development of the theory of the astrophysical processes of formation of stellar mass black holes. Our estimate of the gravitational binding energy released by core collapse supernovae (entry 8.3) is comparable to the energy released in the formation of the massive black hole quasar remnants, and it is not very much less than the upper bound from neutrino detectors. A detection may be feasible, and would complete another check of the cosmic energy transactions.

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