Write to Firebase database only with authenticated users android

I am trying to write to Firebase from android. I only want authenticated users to be able to write to the database. How do I do this?

Here is my registering fragment that attempts to write to the database:

public class register_fragment extends Fragment {

    public static final String FIREBASE_URL = "my_apps_url";

    private FirebaseAuth mAuth;
    private Firebase mRootRef;

    public String studentIdString, emailString, passwordString;

    Snackbar mSnackbar;


    @Nullable
    @Override
    public View onCreateView(LayoutInflater inflater, @Nullable ViewGroup container, @Nullable Bundle savedInstanceState) {

        View view = inflater.inflate(R.layout.register_layout, container, false);
        Button mRegister = (Button) view.findViewById(R.id.green_register_button);
        final EditText mStudentId = (EditText) view.findViewById(R.id.student_id);
        final EditText mEmail = (EditText) view.findViewById(R.id.register_email);
        final EditText mPassword = (EditText) view.findViewById(R.id.register_password);

        mAuth = FirebaseAuth.getInstance();
        mRootRef = new Firebase(FIREBASE_URL);

        mRegister.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
                studentIdString = mStudentId.getText().toString();
                emailString = mEmail.getText().toString();
                passwordString = mPassword.getText().toString();
                registerUser(studentIdString,emailString,passwordString);
            }
        });
        return view;
    }

    @Override
    public void onStart(){
        super.onStart();
        //Check if user is logged in
        FirebaseUser currentUser = mAuth.getCurrentUser();
    }

    private void registerUser(String id, String email, String password){

        mAuth.createUserWithEmailAndPassword(email,password)
                .addOnCompleteListener(getActivity(), new OnCompleteListener<AuthResult>() {
                    @Override
                    public void onComplete(@NonNull Task<AuthResult> task) {
                        if(!task.isSuccessful()){
                            mSnackbar = Snackbar.make(getView(),"Error: "+task.getException(),Snackbar.LENGTH_SHORT);
                            mSnackbar.show();

                        }else{
                            mSnackbar = Snackbar.make(getView(),"Successfully Registered",Snackbar.LENGTH_SHORT);
                            mSnackbar.show();
                            registerUser(studentIdString,emailString);//call method to write to Firebase
                            Intent intent = new Intent(getActivity(), ChapelInProgressActivity.class);
                            intent.putExtra("user",user.getEmail());
                            startActivity(intent);
                        }
                    }
                });
    }

    private void registerUser(String id, String email){

        Map<String, Object> updates = new HashMap<>();
        updates.put("id",id);
        updates.put("email",email);
        FirebaseUser user = FirebaseAuth.getInstance().getCurrentUser();

        mRootRef.child(user.getUid()).updateChildren(updates);//trying to write to Firebase, but does not work
    }

}

I would like the rules for the Firebase database to be:

 ".read": "auth != null",
 ".write": "auth != null"

So only authenticated users can read and write