Draft (Jan. 18, 2010) Executive Summary




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4.2Fundamental cosmology


Hu Zhan (NAOC), Pengjie Zhang (SHAO), Xinmin Zhang (IHEP), Xuelei Chen (NAOC)

Key questions:

1. What is dark matter?

2. What is the nature of dark energy?

3. Do the fundamental physical constants vary as a function of cosmic time?

Cosmology is one of the central drivers of astronomical research throughout the human history. Advances in instrumentation have led to revolutions in our fundamental understanding of the universe. Likewise, TMT will be well poised to shed light on the most profound questions in cosmology of the new century, such as the nature of dark matter and dark energy.


4.2.1Nature of dark matter


Even though dark matter was first proposed a long time ago (Zwicky 1933) to explain the missing mass in galaxies and the Coma cluster, it has thus far evaded detection except indirectly through its gravitational effects on astronomical bodies. Meanwhile, there have been tremendous advances in particle theories of dark matter as well as laboratory experiments for detection and production of dark matter particles. Properties of dark matter particles, such as its mass and interaction cross-section, can have a progressively larger effect on dark matter distribution on smaller and smaller scales, which will be easily accessible by TMT.

The leading candidates of the dark matter particle studied widely in the literature are the weakly interacting massive particles (WIMPs, e.g., Jungman, Kamionkowski, & Griest 1996), for example the lightest neutralino in the supersymmetric standard model with R parity. During the evolution of the Universe, the WIMPs can be generated thermally like the cosmic background of the photons or non-thermally (Acharya et al. 2009).



Thermally generated relic WIMPs behave like the cold dark matter (CDM). They froze out of equilibrium with other species when WIMP annihilation became inefficient (e.g., when the universe cooled to a temperature of the order of the WIMP mass). Non-thermally produced relic WIMPs could be realized in various ways, for instance by decay of cosmic string loops, or decay of long-lived particles, or a low re-heating temperature in inflationary cosmology. Compared to the thermal WIMPs, the non-thermal WIMPs allow a larger annihilation rate into leptons and could make dark matter warm due to the large boost of velocity when generated. Another example for warm dark matter is a light particle with its mass around 1 keV in thermal distribution.

Figure 2


Figure 2: Power spectra of thermal WIMPs (dashed line), non-thermal WIMPs (solid line), and warm thermal WIMPs with a mass of 1 keV (dotted line). From Lin et al. (2001).
shows the suppression of the small-scale matter power spectrum in non-thermal and warm thermal WIMP models relative to the standard CDM model. The amount of suppression is of a few orders of magnitude at scales of a few hundred kpc. Precise measurements of the matter power spectrum at these scales could potentially distinguish different WIMP models, though the scales involved are too small to models, though the scales involved are too small to be studied with galaxy two-point statistics. TMT will meet the challenge through alternative routes described below. The results would be highly complementary to any experiments for direct and indirect detections as well productions of dark matter particles.

Dark matter halo profile

It is well known from N-body simulations that CDM halos follow a universal NFW (Navarro, Frenk, & White 1997) profile, which has a cuspy center. Depending on its scattering and self-annihilation cross-section, dark matter particles could form different amount of substructures and, possibly, a central core. Hence, measurements of dark matter density profiles can be used to place constraints on dark matter interaction cross-sections. Dark matter substructures are difficult to detect to high completeness for an individual halo, so one may need a large sample for statistical detection. To measure the central density profile, it is better to use galaxy clusters, dwarf galaxies, and low surface brightness galaxies, whose center is less dominated by baryonic components, though one could still model and fit different components of normal galaxies with sufficiently high signal-to-noise data.

TMT can measure halo density profiles with lensing and kinematics. For galaxy clusters, strong lensing on arcmin scale is the best way to probe the inner profile. For instance, the central image of a multiply lensed galaxy can place a strong constraint the central density profile (see Tyson, Kochanski, & Dell’Antonio 1998). Stellar kinematics in dwarf spheroidal galaxies offers another unique probe of dark matter halos. It is found with a sample of 18 Milky Way satellites that these galaxies have a common mass of 107 solar masses within 300 parsecs, which rules out thermal warm dark matter candidates lighter than about 1 keV (Strigari et al. 2008). The TMT IRIS IFU instrument will be well suited for such studies; it would extend measurements of dwarf spheroidals’ stellar velocity dispersion beyond the Milky Way and could place tighter constraints on dark matter properties with a much larger sample.

Small-scale power spectrum from the Ly forest

As seen in Figure 2, one needs precise measurements of the matter power spectrum at scales of a few hundred kpc to distinguish different dark matter candidates. So far, such small-scale measurements can only be achieved with the Ly Forest, which is a series of Ly absorption lines in QSO spectra with neutral-hydrogen column densities of 1012—1017 cm−2 (Rauch 1998). These lines are resulted from absorptions by the diffusely distributed and photoionized intergalactic medium, which traces the underlying mass field at low overdensities (e,g., Cen et al. 1994; Zhang, Anninos & Norman 1995; Bi & Davidsen 1997). Therefore, the Ly forest can be used to measure the matter power spectrum on small scales and constrain cosmology (e.g., Croft et al. 1998; McDonald & Miralda-Escudé 1999).

For each line of sight to a QSO, the Ly forest can sample the density field nearly continuously in one dimension. The TMT HROS instrument could sample enough QSO spectra in a large volume, so that one could obtain a more complete picture of the universe and tighter constraints on cosmological parameter using the Ly forest. It is noted that BOSS (SDSS III) and BigBOSS plan to measure baryon acoustic oscillations with dense Ly forest sampling at spectral resolution of 2000. However, many observational and astrophysical effects on the Ly forest, e.g., continuum fitting (Hui et al. 2001), the UV ionization background (Meiksin & White 2004), metal-line contaminations, etc., would require much higher resolution spectra to be disentangled from underlying matter fluctuations.

4.2.2Nature of dark energy


The accelerated cosmic expansion (e.g., Riess et al. 1998; Perlmutter et al. 1999) has led to yet another puzzle – dark energy. Like dark matter, dark energy is thought to be connected to fundamental physics, maybe at even more profound level. However, unlike dark matter, whose gravitational effect is detected in objects as small as galaxies, dark energy might not have appreciable effects on scales much smaller than the Hubble radius. One must bear in mind that dark energy is only one class of explanation for the cosmic acceleration. Another widely discussed possibility is that laws of gravity might depart from four-dimensional general relativity (GR) on very small or very large scales. TMT, with its powerful imaging and spectroscopic capabilities, can realize a number of tests for gravity and dark energy models.

Very high redshift type Ia supernovae for dark energy and curvature

Dark energy constraints from type Ia supernovae (SNe Ia) depend the prior on the mean curvature of the universe (Linder 2005; Knox, Song, & Zhan 2006), because the sensitivity of the luminosity distance to curvature is somewhat degenerate with the sensitivity to the dark energy equation of state (EOS) parameter wa where the EOS is parametrized as w = w0 + wa (1 - a) (see Figure 3) With only low redshift SNe Ia, it is hard to break the degeneracy. However, as shown in Figure 3, high redshift luminosity distances are mostly sensitive to curvature and, hence, can constrain curvature very effectively, which in turn helps determine the EOS parameters. The mean curvature itself is of great theoretical interest as well. Even though inflation flattens the universe, it generally predicts a residual mean curvature of the order of 10-5. There may be a 10% chance to have a mean curvature of the order 0.001 (Freivogel et al. 2006), which is within the reach of future surveys (Knox, Song, & Zhan 2006).

B


Figure 3: Sensitivity of the luminosity distance to the mean curvature and dark energy equation of state parameters w0 and wa. From Zhan (2006).
ecause of its huge light collecting area and IR capability, TMT could easily obtain spectra of SNe Ia up to z ~ 4. To discover these high redshift SNe Ia, one would need a large field-of-view optical-to-NIR instrument to conduct a dedicated survey of at least a few square degrees, which might not be the best use of TMT. Fortunately, other surveys, such as the Large Synoptic Survey Telescope Deep Drilling Survey (ugriz ~ 28 magAB, y ~ 26.8 magAB) and the Chinese Kunlun Dark Universe Survey Telescope (in NIR bands), could provide alerts of potential candidates for spectroscopic follow up. Combining with low redshift SNe Ia from other surveys, TMT could investigate possible evolution of SN Ia population, constrain the mean curvature to 10-3, and provide complementary constraints on dark energy EOS parameters. Furthermore, even though dark energy is thought to be subdominant at high redshift, there is no measurement to prove one way or another. SNe Ia from TMT could in principal be used to study the behavior of dark energy at high redshift.

Testing GR at cluster scale and above

Testing GR in the cosmos is of crucial importance not only in understanding gravity, but also in understanding dark matter and dark energy (Zhang et al. 2007). TMT is possible to perform several tests of GR at cluster scale and above simultaneously, none of which has reached 10% accuracy. With a dedicated spectroscopic survey of a few square degrees, overlapping with existing or then concurrent lensing surveys such as CFHTLS, Pan-STARRS, and LSST, the discriminating power between alternative gravity models will be significantly improved. The key requirement is to measure spectroscopic redshifts of galaxies to z~1-2 or higher and ~100 type Ia supernovae to even higher redshift.



  1. Measuring the parameterized post-Newtonian (PPN) parameter gamma at cluster scale.

The post-Newtonian parameter gamma quantifies the difference between the cluster lensing mass and dynamical mass, which vanishes in GR. In combination with lensing surveys such as CFHTLS, Pan-STARRS, and LSST, TMT will be able to perform such test. With optical and near-IR spectrometers, TMT can significantly improve the measurement accuracy of both masses and thus improve the robustness of the PPN measurement.

To robustly measure the cluster dynamical mass, the rms error in member galaxy velocity measurement should be controlled to be less than 100 km/s, corresponding to a ~1% statistical error in cluster mass. A cluster at is of a few arc-minutes in diameter, with ~ galaxy members. WFOS, with 40 square arc-minute field of view and the ability to measure 1500 spectra simultaneously, is suitable for this task. With redshift measurement of more than ~100 galaxy members, the model uncertainties in cluster dynamical mass reconstruction will be significantly reduced.

A big uncertainty in cluster lensing mass reconstruction through strong and weak lensing is the redshift uncertainty of source galaxies, a large fraction of which lies at redshift beyond 1. With both the optical and near-IR spectrometers, TMT will be able to measure the redshifts of galaxies along the sightline of galaxy clusters and thus eliminate this uncertainty. Another uncertainty is errors in the lensing kernel, which is sensitive to errors in the distance. In combination with the distance measurement from SNe Ia in the same field, the lensing kernel can be calculated in a self-consistent way.

With ~100 massive galaxy clusters in the field, TMT is likely able to push the gamma measurement to the limit of systematical errors. Given the large number of member galaxy redshifts, it is possible to diagnose and reduce some systematical errors, such as the galaxy velocity bias and the velocity anisotropy.



  1. Measuring the structure growth and testing the GR consistency relation

With a million redshifts to z~1-2 in a few square degrees, the 3D galaxy power spectrum can be measured with more than 1000 independent modes in the linear and mildly non-linear regime. This allows robust measurement of redshift distortion and the reconstruction of large scale peculiar velocity. The structure growth of the universe can be measured with ~10% accuracy. This measurement alone is already able to test GR and discriminate it from several alternative gravity models.

In combination with the measurement of the expansion rate from SNe Ia, one can perform a direction test on the GR consistency relation between the expansion rate and the structure growth rate. It reads



.

The left hand side can be measured from the redshift distortion and the right hand side can be measured from SNe Ia.

It is also possible to perform further tests of GR. For example, in combination with the weak lensing measurement, we can test the Poisson equation at cosmological scales. This allows us to measure the quantity and further probe the nature of gravity.

4.2.3Constancy of fundamental constants


Constancy of fundamental physical constants, such as the fine structure constant and speed of light, constitutes another class of interesting tests. Since the currently well established cosmological frame work is based on the constancy of these constants, any definitive detection of departure from constancy will lead to fundamental changes of our view about the universe. Note that running coupling constants are no stranger to particle physics, but departure from constancy over time at the same energy level would require an exceptional explanation.

The Ly forest mentioned above can be used for such investigations, though hydrogen Ly lines become a contaminant (for a review, see Uzan 2003). For the fine structure constant , one ideally needs a line transition that is not sensitive to for measuring redshift and another that is very sensitive to for determining the change in . Current limit on the variation of below redshift 2.5 is  ~10-5, which requires spectral resolution R ~ 40000. With TMT HROS, one could extend the measurements to much higher redshift.



Possible TMT programs:

  1. A survey of stellar kinematics of several thousand dwarf spheriodals with TMT/IRIS to study dark matter properties.

  2. A legacy survey of TMT/WFOS of galaxies in a few squares of degrees to measure the growth of structure and test General Relativity.

  3. A survey of galaxy kinematics of several thousand clusters with TMT/WFOS to measure PPN parameter gamma.

  4. TMT/HROS of observations of selected quasars at very high resolutions to study the nature of dark matter and the variation of fundamental constants.


China’s strengths and weakness in this area:
There are a healthy group of theorists (IHEP, NAOC, SHAO) working on the nature of dark matter, dark energy, and modified gravity. However, observational expertise, particularly on the 8-10m class telescopes is lacking, and further PhD students should be trained in these areas.

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